LIBRARY 

OF  THE 

UNIVERSITY  OF  CALIFORNIA. 


Class 


ELEMENTS    OF    PHYSICS 


BY 


FERNANDO   SANFORD 

Professor  in  Lelcind  Stanford  Junior  University 


NEW  YORK 

HENRY  HOLT  AND  COMPANY 
1904. 


Copyright,  1902, 

BY 
HENRY  HOLT  &  CO. 


ROBERT   DRUMMOND,    PRINTER,    NEW   YORK 


PREFACE 

"  MAN  may  have  at  his  fingers'  ends  all  the  accomplished 
results  and  all  the  current  opinions  of  any  one  or  of  all  the 
branches  of  science,  and  yet  remain  wholly  unscientific  in  mind; 
but  no  one  can  have  carried  out  even  the  humblest  research 
without  the  spirit  of  science  in  some  measure  resting  upon  him. 
And  that  spirit  may  in  part  be  caught  even  without  entering 
upon  an  actual  investigation  in  search  of  a  new  truth.  The 
learner  may  be  led  to  old  truths,  even  the  oldest,  in  more  ways 
than  one.  He  may  be  brought  abruptly  to  a  truth  in  its  finished 
form,  coming  straight  to  it  like  a  thief  climbing  over  the  wall ; 
and  the  hurry  and  press  of  modern  life  tempt  many  to  adopt 
this  quicker  way.  Or  he  may  be  more  slowly  guided  along  the 
path  by  which  the  truth  was  reached  by  him  who  first  laid  hold 
of  it.  It  is  by  this  latter  way  of  learning  the  truth,  and  by  this 
alone,  that  the  learner  may  hope  to  catch  something  at  least  of 
the  spirit  of  the  scientific  inquirer."* 

THREE  hundred  years  ago  a  new  method  of  acquir- 
ing knowledge  was  given  to  the  world  by  Gilbert,  in 
England,  and  by  Galileo,  in  Italy.  When  this  method 
was  adopted  by  investigators,  Physical  Science  was 
still  in  its  infancy,  while  other  branches  of  human 
knowledge,  as  Philosophy,  Literature,  and  Art,  had 
apparently  reached  their  highest  possible  achievements. 
Since  that  time,  the  development  of  Physical  Science 

*From  the  Presidential  Address  by  Sir  Michael  Foster,  K.C.B., 
F.R.S.,  to  the  British  Association  for  the  Advancement  of  Science, 
Dover,  Sept.  13,  1890. 

iii 

168305 


iv  PREFACE 

has  been  the  most  remarkable  phenomenon  of  the 
world's  history. 

This  new  method  of  acquiring  knowledge,  which 
may  be  called  the  scientific  method,  has  been  often 
discussed,  and  there  is  substantial  agreement  as  to  the 
steps  which  it  involves.  They  are:  (i)  The  acquisition 
of  individual  facts,  either  by  general  observation  or  by 
the  method  of  artificial  observation  known  as  experi- 
mentation; (2)  Generalization,  the  statement  of  a 
general  relation  which  seems  to  exist  between  these 
individual  facts;  (3)  Deduction,  the  making  of  indi- 
vidual inferences  based  upon  the  generalization  of  the 
second  step;  and  (4)  Experimentation  to  test  the 
accuracy  of  these  inferences.  A  method  which  starts 
in  the  middle  of  the  process  by  stating  the  generaliza- 
tion and  requiring  the  pupil  to  make  the  deductions 
only,  may  give  a  good  training  in  deductive  reasoning 
— in  Algebra  and  Geometry — but  it  cannot  teach 
Physics  nor  give  a  training  in  the  methods  of  Physics. 
A  method  which  makes  the  generalizations  and  deduc- 
tions and  calls  upon  the  pupil  to  verify  these  deductions 
by  experiment  likewise  gives  training  in  but  one  step 
of  the  process.  And  a  method  which  teaches  the 
subject-matter  of  Physics  from  the  text-book  alone  and 
provides  a  list  of  unrelated  experiments  to  be  performed 
for  the  purpose  of  training  the  observing  powers  or 
giving  skill  in  manipulation  misses  the  whole  process. 

The  present  text-book  is  a  result  of  the  attempt  of 
the  writer  to  apply  this  scientific  method  in  all  its 
steps  to  the  teaching  of  Physics.  It  does  not  contain 
as  many  laboratory  experiments  as  are  recommended 
in  some  books,  but  most  of  those  it  does  contain  are 
vital  to  the  successful  teaching  of  the  book.  No  ex- 


PREFACE  v 

periments  are  admitted  for  any  reason  except  that  they 
are  needed  for  teaching  the  subject  as  outlined.  Ac- 
cordingly, they  are  not  selected  because  they  are  quan- 
titative or  qualitative  in  character,  or  because  they  are 
easy  or  difficult  to  perform.  The  lecture-room  method 
of  imparting  knowledge  is  believed  by  the  writer  to  be 
the  poorest  of  all  methods  with  elementary  students, 
and  the  book  is  not  prepared  with  the  idea  that  it  will 
need  supplementing  by  a  lecture  course.  Neither  is  it 
intended  to  dispense  with  the  services  of  a  teacher.  In 
fact,  it  has  been  prepared  especially  for  the  teacher  who 
has  had  an  adequate  training  in  the  physical  labora- 
tory, and  it  is  not  likely  to  succeed  with  any  other 
teacher. 

In  the  arrangement  of  the  subject-matter  a  consider- 
able departure  has  been  made  from  the  order  of  other 
books,  but  this  arrangement  has  not  been  adopted 
without  careful  tests  by  the  writer  and  others.  The 
great  distinction  between  the  Physics  of  the  present 
and  that  of  the  past  generation  lies  in  the  substitution 
of  the  concept  of  energy  for  the  old  notion  of  forces. 
The  attempt  is  here  made  to  base  Mechanics  upon  the 
energy  concept  from  the  beginning,  and  to  assign  to 
the  notion  of  force  the  meaning  which  it  holds  in 
modern  Physics.  In  the  treatment  of  the  properties  of 
bodies,  the  order  adopted  seems  justified  by  the  relative 
simplicity  of  the  gaseous  state  of  aggregation  as  com- 
pared with  the  liquid  or  solid  state.  Here,  too,  more 
stress  is  laid  on  the  kinetic  gas  theory  than  is  usual  in 
an  elementary  text-book,  but  this  seems  to  be  war- 
ranted by  the  great  importance  of  the  theory  in  modern 
Physics  and  its  bearing  on  the  modern  theory  of  Heat. 

The   greatest    departure  from  established   usage    in 


VI 


PREFACE 


elementary  text-books  has  been  made  in  the  subject 
of  Optics.  Here  the  attempt  has  been  made  to  develop 
the  Geometrical  Optics  from  the  beginning  without 
making  use  of  the  fiction  of  rectilinear  propagation. 
In  the  writer's  own  experience,  this  greatly  simplifies 
the  subject,  especially  in  the  study  of  Refraction. 
While  the  experiments  on  interference  are  not  usually 
given  in  a  high-school  course,  they  offer  no  greater 
difficulties  to  the  pupil  than  the  ordinary  experiments 
in  other  subjects,  and  they  are  essential  to  an  under- 
standing of  the  undulatory  theory  of  Light.  The 
experiments  on  the  measurement  of  wave-length  in 
both  Sound  and  Light  have  seemed  to  the  writer  a  very 
important  part  of  the  course.  The  treatment  here 
given  to  the  subject  of  the  refractive  index  has  also 
been  justified  by  its  use  for  several  years  with  the 
writer's  own  pupils. 

While  the  course  as  here  outlined  cannot  be  taught 
without  a  suitably  equipped  laboratory,  it  is  believed 
that  the  necessary  expense  of  fitting  up  a  laboratory 
for  its  teaching  is  as  small  as  for  any  other  laboratory 
course  of  high-school  grade  which  has  been  suggested. 

F.  S. 

LELAND  STANFORD  JUNIOR  UNIVERSITY, 
June  7,  1902. 


TABLE  OF  CONTENTS 

PART  I 

MECHANICS 

FUNDAMENTAL   DEFINITIONS 


Physics 

The  Physical  Universe 

Matter 

Energy 

Work 

Measurement  of  Work 


MACHINES 


The  Lever      .  ...       2 

The  Lever  as  a  Machine  ...  4 

Classes  of  Levers        .  .....       4 

Moment    ...  5 

Mechanical  Advantage  «  •  -5 

Problems 

The  Fixed  Pulley       . 

Levers  of  the  Second  and  Third  Classes  6 

The  Movable  Pulley 

Systems  of  Pulleys 

Mechanical  Advantage  of  Systems  of  Pulleys 

The  Inclined  Plane  9 

Modification  of  Lever,  Pulley,  and  Inclined  Plane     .  .      10 

The  Wheel  and  Axle  ....  .10 


viii  TABLE  OF  CONTENTS 

PAGE 

The  Windlass             .             .             .             .             .  .             .11 

The  Screw             .             .             .             .             .  u 

POWER 

Definition              .,          .             .             .             .  .             »           n 

EFFICIENCY 

Definition      .             »             .          :  .    J        .             .  .             .12 

Problems                .             .             .             .             .  »           12 

GEARING 

Use  of  Gearing           .            .            .             .             .  .             .12 

Problems  .                           .             »             .             .  ...           12 

CENTER   OF   GRAVITY 

Definition       .             .             ,             .             .             .  .                  13 
To  Find  the  Center  of  Gravity  of  an  Irregular  Solid  .         -    »           14 
To  Find  the  Weight  Moment  of  a  Bar  Supported  from  a  Point  Out- 
side its  Center  of  Gravity            .             .             .  . »    '.         -14 

STABILITY 

Conditions  of  Equilibrium             .             .             .  *            15 

Stable  and  Unstable  Equilibrium       .             .             .  .             .15 

Neutral  Equilibrium          .             .             .             .  .             .16 

Examples       .             .             .             .             .             .  .             .16 

Measure  of  Stability          .             .             .             .  .             .16 

Problems        .......  .16 

THE  PENDULUM 

Energy  of  a  Swinging  Pendulum               .             .  .             .17 

Potential  and  Kinetic  Energy  of  the  Pendulum          .  .             .18 

Isochronism  of  the  Pendulum        .             .  .             .20 

Relation  of  Time  of  Vibration  to  Length  of  Pendulum  .              .     20 
Relation  of  time  of  Vibration  to  Weight  and  Material  of  Pendulum       21 

The  Seconds  Pendulum          .             .             .             .  .              .21 

Simple  and  Compound  Pendulums            .             .  .             .21 


TABLE  OF  CONTENTS  ix 

1'AGK 

To  Find  the  Equivalent  Length  of  a  Compound  Pendulum  .  .     22 

Center  of  Suspension  of  a  Pendulum         ....  22 

Center  of  Oscillation  of  a  Pendulum               .              .             .  .22 

Length  of  a  Compound  Pendulum             ....  23 

Problems         .             .              .              .              .              .             .  -23 

Persistence  of  Plane  of  Vibration  of  a  Pendulum               .             .  23 

Foucault's  Pendulum  Experiment       .             .             .             .  .     23 

GRAVITATION 

Definition  .  .  .  ...  .  .24 

Nature  of  Gravitation  Unknown         .             .             .             .  .     25 

Gravitation  and  Time  of  Vibration  of  a  Pendulum           .             .  25 

Light  and  Heavy  Bodies  Fall  with  Same  Velocity     .             .  .     25 

The  "  Guinea  and  Feather  Tube  "           ....  26 

MASS 

Potential  Energy  of  a  Body  Proportional  to  its  Weight         .  .     26 

Kinetic  Energy  of  a  Moving  Body  Independent  of  its  Weight      .  27 

Definition  of  Mass      .              .              .              .             .              .  -27 

Indestructibility  of  Mass  ......  27 

Relation  of  Weight  to  Mass   .             .             .             .             .  .28 

INERTIA 
Definition  .  .  .  .  .  .  .28 

FALLING    BODIES 

Gravitation  and  Falling  Bodies          .             .             .             .  .29 

Atwood's  Machine             ......  29 

Experiments  with  Atwood's  Machine              .             .             .  -3° 

ACCELERATION 

Definition  of  Acceleration  .  .  .  .  .31 

Uniform  Acceleration              .                           .             .             .  •     3* 

Positive  and  Negative  Acceleration                         ...  32 


x  TABLE  OF  CONTENTS 

PAGE 

Acceleration  of  Falling  Bodies            .              .             .  *              .     32 

Magnitude  of  Gravitation  Acceleration    .             .  »             ,           32 

Problems        .             .             .             .             ...  -33 

UNIVERSALITY   OF   GRAVITATION 

Gravitation  Acceleration  of  the  Moon       .             .  '..             .           33 

Gravitation  Accelerations  of  the  Planets  and  Satellites          .  -34 

Newton's  Law  of  Gravitation        .             .             .  .34 

FORGE 

Definition  of  Force     .             .             .             .             .  .             -35 

Measurement  of  Force      .             .             .             .  «             .           35 

Newton's  Laws  of  Motion       .             .             .             .  .                   36 

Momentum           '.             .             .             .             .  '•.    .                   37 

The  Force  Equation  .             .*            .             .             .  .             .38 

Definition  of  Constant  Force         .             .             .  '.,,             .           38 

FORCE   UNITS 

ThePoundal               .             ..            .             .            ..;  .         .    ,         .38 

The  Dyne             .             .             .  <          ;             .    ,  .            .           38 

Problems        .             .             .             .'            .         t  .  .             -39 

ACTION   AND    REACTION 

Definition  of  Action  and  Reaction      .             .             .  .             -39 

Equality  of  Action  and  Reaction               .             .  .             ;           40 

Restatement  of  Newton's  Third  Law         .    .             .  .             .40 

Direction  of  Momentum    .             .             .             .  .             .41 

Momentum  of  Rebounding  Ball          .             .             .  .              .41 

Persistence  of  Momentum  in  Elastic  Impact         .  .             ,           41 

FORCE   AND  WORK 

Force  one  Factor  in  Work     .             .             .             .  .             .42 

Equation  for  Force  and  Work       .             .             .  .             .43 

The  Erg  .     43 

Problems  on  Force  and  Work       .              .  .              .44 

Potential         .             .             .             .             .             .  .             '44 


TABLE  OF  CONTENTS  xi 
GENERAL    EQUATIONS    OF    MECHANICS 

PAGE 

Force              .             .             .             .             .             .  .             -45 

Velocity   .             .             .             .             .             .             .  .45 

Acceleration  .              .              .             .             .             .  .             -45 

Distance  .......  45 

Momentum     .             .             .             .             .             .  .             -45 

Work         .                       .'."'        .                          .  -45 

Problems         .             .             .             .             .             .  .             .46 

COMPOSITION   AND   RESOLUTION   OF  MOTIONS 
AND    FORCES 

Composition  of  Motions          .             .             .             .  .             .46 

Resultant  Motion            '  .                           .              .             .  .           47 

Graphical  Composition  of  Motions     .              .              .  .             .     4^ 

The  Parallelogram  Law    .             .             .             .             .  .           49 

The  Triangle  Law     .             .              .             .             .  .             .     50 

Composition  of  More  than  Two  Velocities             ...  .           50 

Composition  of  Forces             .             .             .             .  .             •     5 r 

Resolution  of  Forces,  Velocities,  and  Accelerations          .  .           53 

Problems         .             .             .             .             .             .  .             -54 

RESOLUTION  OF  CIRCULAR  MOTION 

Circular  Motion  a  Resultant  Motion  .             .             .  .             '54 

Equation  for  the  Acceleration  Component             .             .  .           55 

Centripetal  Force.     Centrifugal  Force          .             .  .             .56 

Problems  in  Circular  Motion        .             .             .             .  .58 

PART  II 
PROPERTIES  OF  BODIES 

STATES   OF   AGGREGATION 

Three  Kinds  of  Bodies            .  •             •     59 

ELASTICITY 

Definition  of  Elasticity           .  .     59 
Perfect  Elasticity                ......            60 


xii  TABLE  OF  CONTENTS 


Rigidity          .  .  ...  •  .  »  .60 

Fluids       ........  60 

Two  Classes  of  Fluids  .  .  .  .  .60 

Simplicity  of  Gaseous  State          .  .  .  .  ,60 


THE  GASEOUS  STATE 
PROPERTIES   OF  GASES 

Indefinite  Expansion               .             .             .             .  .             .60 

The  Air  Pump      .             .             .             .             .  .             .61 

Weight  of  Air             .             .             .             .             .  .              .63 

Problems  .             ...             .             ...  .             .64 

Density  of  Air           .             .             .             .             .  .             .     64 

Specific  Gravity  of  Gases              .             ...  .             .64 

To  Find  the  Specific  Gravity  of  Illuminating  Gas     .  .             .64 

Pressure  of  the  Atmosphere          .             .             .  .             »           65 

To  Show  the  Pressure  of  the  Atmosphere      .             .  .             -65 
Measurement  of  Atmospheric  Pressure     ....           67 

The  Barometer            .             .             .             .             .  .             .68 

Atmospheric  Pressure  and  Respiration     .             .  .             .70 

Pressure  of  Fluids  Within  the  Body  .         .     .             ,  .  •          .71 

Experiment  with  Hand  Glass       .             .             »  •>,  .             .           72 

Problems        .             .             .             .             .             .  .             «     72 

The  Siphon           ...             .             .  .             .            74 

Pumps             .             .             .             .             .             .  .             -75 

LAWS  OF  GASES 

Relation  of  Gaseous  Volume  to  Pressure        .             .  .             -77 

Boyle's  Experiment           ......  77 

Boyle's  Law  .             .             .             .             .             .  .             .     78 

Problems                .......  79 

Relation  of  a  Gas  Volume  to  Temperature    .             .  .             -79 

Measurement  of  Heat  Expansion  of  a  Gas             .  .             .           80 

Law  of  Charles           .             .             .             .             .  .             .81 

Absolute  Temperature       .             .             .             .  .             .81 

Change  of  Pressure  with  Change  of  Temperature      .  .              .82 

The  Gas  Equation             .             .             .             .  .             .           82 


TABLE  OF  CONTENTS  xiii 

PAGE 

Problems         .  .  .  ,  .  .  .83 

Work  Done  by  Expanding  Gas    .....  84 

Problems         .  .  .  .  .  *  .  .84 

Universality  of  Gas  Equation       .  .  .  .85 

Dalton's  Law  .  ...  .     851 

NATURE   OF   GASES 

All  Gases  Have  Similar  Structure      .             .  .             .             .86 

Two  Possible  Theories  of  Gas  Structure  ....  86 

Comparison  of  Two  Theories             .             .  .             .             .86 

Molecules  and  Atoms        ......  87 

Chemical  Evidence  of  Molecules  and  Atoms  .             .             -87 

Diffusion  of  Gases             .                          .  .             .             .88 

Diffusion  of  Gases  through  a  Porous  Partition  .             .             ,88 

Avogadro's  Theory           .             .             .  .             .             .90 

Cause  of  Gaseous  Pressure     .             .             «  .             .             .     91 

Pressure  Within  a  Gas  Equal  in  All  Directions  ...            94 

Buoyant  Force  of  a  Gas          .             .             .  .             .             -94 

Molecular  Weights            .  .             .             .95 

Molecular  Velocities  and  Pressure      .             .  .             .             -95 

The  Kinetic  Gas  Theory              .             .  .             .             .96 


THE   LIQUID   STATE 
PROPERTIES  OF  LIQUIDS 

Cohesion     .             .            —  .             .             .             .             .  .96 

Vapor  Pressure  of  a  liquid            .                          .             .  •           .  97 

Measurement  of  Vapor  Pressure  of  a  Liquid               .             .  -97 

Comparison  of  Liquid  and  Gaseous  Properties     ...  98 

Elasticity  of  Form  in  Liquids              .             .             .             .  -99 

Form  of  a  Liquid  Removed  from  Gravitation       ...  99 
Contraction  of  Surface  Film  of  Liquids           ....    100 

Experiments  with  Surface  Films               ....  100 

Formation  of  Surface  Film  by  Cohesion         .             .             .  .    101 

Influence  of  Curvature  of  Surface  on  Surface  Tension      .             .  103 

Surface  Tension  on  Soap  Bubble       .  .   103 

Pressure  of  Surface  Tension  on  Opposite  Sides  of  a  Soap  Film    .  104 


xiv  TABLE  OF  CONTENTS 

PAGE 

Measurement  of  Surface  Tension        .....   105 

Surface  Tension  in  Capillary  Tubes  .             .             .             .          106 

Measurement  of  Capillary  Constants  ....    106 

Surface  Tension  of  Mercury          .  .             .             .             .          107 

Magnitude  of  Cohesion           .  .             .             .             .    108 

Compressibility  of  Liquids            .  .             .          -  .             .          109 

Viscosity        .             .             .  .             .             .             .   109 

Diffusion  of  Liquids          .             .  .             .             .             .         1 1 1 

Influence  of  Viscosity  on  Diffusion    .  .             .             .             .    1 1 1 

Diffusion  through  Porous  Membrane  .             .             .             ,          1 1 1 

Osmosis          .           ..             .             .  .             .             .             .112 

Osmotic  Pressure               .             .  .             .             .             .112 

Evaporation   .             .             .             .  .             .             .             .    113 

Boiling      .                           .         •    .  .             .             .             ,          114 

Vapor  Pressure  of  a  Boiling  Liquid  .  .             .             .             .114 

Condensation        .              .             •.  .             .             .             .115 

MECHANICS   OF   FLUIDS 

Conditions  of  Equilibrium  in  Fluids  .  .  .  .  .115 

Transmission  of  Pressure  .  .  .  .  .116 

The  Hydraulic  Press  .  .  .  .  .  •    JI7 

Gravitation  Pressure  Within  a  Liquid      .  .  ,  .          1 18 

Measurement  of  Gravitation  Pressure  Within  a  Liquid          .  .118 

Pressure  Upon  any  Point  Within  a  Liquid  is  the  Same  in  All  Direc- 
tions .  »  .  .  .  .  .  .119 

Downward  Pressure  of  a  Liquid  Column  Independent  of  its  Shape  .    120 
Pressure  of  a  Liquid  Upon  the  Sides  of  the  Containing  Vessel     .          121 
Average  Pressure       .  .  .  .  .  .  .121 

Buoyant  P'orce  of  a  Liquid  .  .  .  .  .122 

Loss  of  Weight  of  a  Body  Immersed  in  Water  .  .  .    123 

Floating  Bodies    .  .  .  .  .  .          124 

Principle  of  Archimedes         ......    125 

Density  and  Specific  Gravity  of  Liquids  and  Solids         .  .          125 

Measurement  of  Density  by  Principle  of  Archimedes  .  .    125 

Use  of  Specific- gravity  Bottle       .  .  .  .  .126 

Problems        ....  .  .   126 


TABLE  OF  CONTENTS  xv 

THE   SOLID   STATE 
PROPERTIES   OF  SOLIDS 

PAGE 

Change  from  Liquid  to  Solid  State    .  .             .             .             .   127 

Structure  of  Solids             .             .  .             .             .             .         127 

Properties  of  Crystalline  Solids          .  .              .              .              .    128 

Isotropic  and  Anisotropic  Bodies  .            . .             .             .          129 

Equilibrium  of  Solid  and  Liquid  States  .              .             .              .129 

Cohesion  between  Solid  Surfaces  .                                                 129 

FRICTION    BETWEEN   SOLID   SURFACES 
Cause  of  Friction       .......   130 

Coefficient  of  Friction       ......         130 

Coulomb's  Laws  of  Friction  .  .  .  .  .    131 

Rolling  Friction    .......          132 

Use  of  Lubricants       .  .  .  .  .  .  .132 

ELASTICITY  OF   SOLIDS 

Elasticity  of  Compression       .  .  .  .  .  .  133 

Rigidity  ........  133 

Hooke's  Law  .......  134 

Limits  of  Perfect  Elasticity  .....  134 

Change  of  Density  in  Solids  .....  135 

Elastic  Impact      .......  135 


PART  HI 
HEAT 

ORIGIN  OF  OUR  KNOWLEDGE  OF  HEAT 

The  Temperature  Sense         .  '  •     •     .  •*          .  .  .  .   137 

Definition  of  Heat  .  .  .  .  .  .         137 

Other  Means  of  Recognizing  Heat     .  .  .  .  .   138 

SOURCES   OF   HEAT 

Importance  of  Sun's  Radiation          .....   138 
Chemical  Sources  of  Heat  .....         138 

Mechanical  Production  of  Heat          .  .  ...  .   138 


xvi  TABLE  OF  CONTENTS 

NATURE    OF    HEAT 

PAGE 

The  Caloric  Theory  .             .             .             .             .  .             .   139 

Count  Rumford's  Experiment       .             .             .  .             .          139 

Davy's  Experiment  .             .             .             .             ,  .             .   140 

Carnot's  Theory  .             .             .             .             .  .             ,141 

Joule's  Determination            .             .             .             .  .             .   142 

The  Conservation  of  Energy         ,             .             .  .          143 

The  Mechanical  Theory  of  Heat        .             „'           .  •             •   i43 

EFFECTS   OF    HEAT 

Expansion      .            ..             .             .             .  .       -  .  ,             .   146 

Heat  Expansion  of  Water             .            .             .  .            ,         146 

Linear  Expansion  of  Solids   .             .             .             .  »             .    147 

Relation  between  Linear  and  Cubical  Expansion  «             .          149 

Coefficients  of  Linear  Expansion        .             .  «             .    150 

Coefficients  of  Cubical  Expansion              .            .  .             .         150 

Problems        .             .             .            «             .             .  .             .   150 

CHANGE   OF   STATE 

Melting              .             .         ...             .             .  .             .   151 

Conditions  of  Equilibrium  of  a  Solid  and  its  Liquid  .             «         151 

Melting  Points            .             .             .             .'             »  ^ ,           .   151 

Disappearance  of  Heat  During  Fusion     .            >.  .    •         »          152 

Change  of  Volume  in  Melting           .             .              .  .                 153 

Influence  of  Pressure  Upon  the  Melting  Point      .  .             .         154 

Energy  Changes  in  Solution              ,'.             .             .  .             .    155 

Freezing  Mixtures             .             .             .             .  .                       155 

Vaporization           "•    .             .             .."           .             .  .              .    155 

Boiling  Points       ,             .          ,  .             .             .  .             .          156 

Lowering  of  Boiling  Point  by  Decrease  of  Pressure  .             -156 

Problems  ...             .             .         ~  »    .  .         158 

Boiling  Points  of  Solutions     •.             .             .             .  .             .    159 

Distillation            .             .             .             .              .  .             .159 

Relation  of  Boiling  Point  of  Solution  to  Concentration  .              .    161 
Sublimation          .......          161 

CONDENSATION    OF  ATMOSPHERIC   VAPOR 

Aqueous  Vapor  in  the  Atmosphere    .....    161 

Formation  of  Dew             ...  162 


TABLE  OF  CONTENTS  xvii 


PAGE 

The  Dew  Point          .             .             .             .             .             .  .162 

Determination  of  Dew  Point        .....  163 

The  Hygrometer       .             .             .             .             .             .  .164 

Formation  of  Frost  .  .  .  .  .  .164 

Condensation  Within  the  Atmosphere             .             .             .  .164 

Formation  of  Clouds          ......  165 

Problems          .             .             ...             .             .  .   166 

CRITICAL  TEMPERATURES  AND   PRESSURES 

Critical  Temperatures             .              ,  .             .             .             .166 

Liquefaction  of  Gases    .                  .  .             .             .             .166 

Table  of  Critical  Constants  of  Gases  ....    167 

Lowest  Known  Temperature        .  .             .             .             .         168 

ENERGY   CHANGES   IN   VAPORIZATION 

Disappearance  of  Heat  During  Vaporization  .  .  .   168 

Cooling  of  Ether  by  Evaporation  .  .  .  .168 

The  Psychrometer     .......   169 


DISTRIBUTION   OF   HEAT 
CONDUCTION 

Definition       .             .             .             .             .  .             .             .   169 

Conduction  in  Solids        -»•            .             .  .             .             .          169 

Law  of  Conductivity              .             .              .  .              .              .   171 

Conduction  in  Liquids      .             .              .  .             .             .171 

Conduction  in  Gases               .             .             .  .             .             .   171 

Table  of  Conductivities    .            . """"  .             .             .         171 

CONVECTION 

Formation  of  Currents  by  Gravitation            .  .             .             .172 

Convection  Currents  in  Water       .              .  .             .             .173 

Importance  of  Convection  Currents  in  Nature  .             .             .    174 

Heating  and  Ventilation  of  Houses           .  .             .             .174 

Questions  on  Convection         .             .             .  .             .             .    175 

RADIATION 

Transference  of  Energy  Through  a  Vacuum  .    176 

Definition  of  Radiation     .             .             .  .             .             .176 


xviii  TABLE  OF  CONTENTS 

PAGE 

Mutual  Transformation  of  Heat  and  Radiant  Energy  .              .176 

Absorption  of  Radiant  Energy     .             .  ••.'.-•>         177 

Selective  Absorption               .             .             ...  .              .    177 

Reflection  of  Radiant  Energy       .             .             .  .             .177 

Relation  between  Radiation  and  Absorption              .  .              .178 

HEAT   MEASUREMENTS 

Two  Kinds  of  Measurements  .  "  .  .  .  .178 

THERMOMETRY 

Definition       ;    .     N  *            .             .             .  .     •       •  »"            .178 

Construction  of  Thermometers      .             .             .  *.             ,          1 79 

Graduation  of  Thermometers             .             .  .             .             .180 

Comparison  of  Fahrenheit  and  Centigrade  Scales  .             .         181 

To  Test  the  Fixed  Points  of  a  Thermometer  .             .             .181 

Calibration  of  Thermometer  Tube            .             .  .             .         182 

CALORIMETRY 

Definition      ........   183 

The  Heat  Unit     .  .  .  '.  .  .  .183 

Heat  Capacity  .  .  .  .  •  •  .183 

Heat  Capacity  of  a  Calorimeter  .  .  .  .  .         183 

Determination  of  Latent  Heat  of  Fusion  of  Ice          .  .  .   184 

Determination  of  Latent  Heat  of  Vaporization  of  Water  .          185 

Specific  Heat  . .  . .  .  .  .  .  .   186 

Determination  of  Specific  Heat  of  Lead  Shot       .  .  .          186 

Determination  of  Specific  Heat  of  a  Liquid  .  .  .186 

Specific  Heats  of  Gases  ......         187 

Relation  between  the  Two  Specific  Heats  of  Air       .  .  .188 

Energy  Value  of  the  Calorie         .....         188 

HEAT   ENGINES 

Definition       ........  189 

The  Steam  Engine  ,  .  .  .  .  .190 

High-pressure  and  Lo\,-pressure  Engines      ....  193 

The  Gas  Engine  .......  193 

Efficiencies  of  Engines            ......  196 

Problems                .......  198 


TABLE  OF  CONTENTS  xix 

PART  IV 

WAVE-MOTION  AND  SOUND 
SOUND 

PAGB 

Scope  of  the  Subject              .....  .   199 

VIBRATION   OF   SOUNDING  BODIES 

First  Law  of  Sound    .             ...              .              .  .    199 

Experiments  on  Sound  Vibration                .   :»                       .             .  199 

Transmission  of  Vibrations  by  Solids,  Liquids  and  Gases     .  .   201 

Vibrations  Not  Transmitted  by  a  Vacuum                         .              .  203 

WAVE-MOTION 

How  Vibrations  are  Transmitted       .....  203 

Wave-motion  in  Spring  Cord        .....  203 

Two  Forms  of  Wave-motion  ......  204 

The  Wave  Machine           ......  205 

Wave-front     .             .             .             .             .             .             .  .  206 

Wave-train           .                          .             .             .             .             .  207 

Wave-length  .......  207 

Relation  of  Wave-length  to  Velocity  of  Propagation        .             .  208 

Relation  of  Wave-length  to  Period  of  Vibration         .              .  .  208 

Wave  Amplitude  .             .  ~*         .         ~~~~^~t'~           .             .             .  208 

Wave  Induction          .             .             .             .             .             .  .  208 

Resonance             .   :         .             .             .             .             .             .  209 

Forced  Vibrations      .              .             .           ,..          .              .  .211 

Reflection  of  Waves          .             .            -.             .             .             .  212 

Interference  of  Waves  by  Reflection  .             .-             .             .  .213 

Standing  Waves    .......  213 

Interference  of  Sound  Waves             -."  .          .             .             .  .  215 

Velocity  of  Wave  Propagation      .....  220 

General  Equation  of  Wave-motion     .              .             .             .  .   222 

Relative  Velocity  of  Waves  in  Air  and  in  Glass  .              .             .  223 

Measurement  of  Relative  Velocities  of  Waves  in  Air  and  Glass  .  224 


xx  TABLE  OF  CONTENTS 

NATURE   OF    SOUND 

PAGE 

Two  Definitions  of  Sound       ....  .   224 

Classification  of  Sounds    ......         224 

Limits  of  Audibility  .             .             .             .  -   225 

MUSICAL   SOUNDS 

Properties  of  Musical  Sounds  .  ...   225 

Intensity  .                           .             .             .             •.             .  .         225 

Intensity  and  Loudness          .             .             .             .             .  .226 

Variation  of  Intensity  with  Distance  from  Source  .         227 

Pitch               .             .             .             .             .             .  -227 

Doppler's  Principle           .             .             .                           »  .         227 

Quality           .             .             .             .            »             •             .  -  228 

Relation  of  Quality  to  Complexity  of  Sound        .»             .  .         228 

Complexity  of  the  Note  of  an  Organ  Pipe      .             .  .   230 

Fundamentals  and  Overtones        .             .             ..           .  .231 

Overtones  in  a  Vibrating  Wire           .                           .  -231 

Overtones  in  Organ  Pipes  •         232 

PHYSICAL   THEORY   OF   MUSIC 

Consonant  and  Dissonant  Tones         ....  .  233 

Cause  of  Dissonance         .            .  <         .             •             •  .         233 

Dissonance  of  Compound  Tones         .             *             .             •  •   233 
Musical  Scales      .......         234 

Musical  Instruments  .             .             .             .             .             .  •   235 

Problems  on  Sound            .             .             .             *             .  •"  •         235 


PART   V 

MAGNETISM   AND   ELECTRICITY 
MAGNETISM 

PROPERTIES    OF    MAGNETS 

Natural  and  Artificial  Magnets  .  237 

Magnetic  Poles      .......         238 

Magnetic  Attractions  and  Repulsions  ....  239 


TABLE  OF  CONTENTS  xxi 

MAGNETIC    PERMEABILITY 

PAGB 

Magnetic  Permeability  of  Iron  .....  239 

THE   MAGNETIC    FIELD 

Definition       .    -          .  .  .  .  .  .  .   240 

Magnetic  Induction  .  .  .  .  .  .         240 

Magnetic  Force  Within  a  Magnet      .....   240 

THE   MAGNETIC   CIRCUIT 

Relation  of  Magnetic  Poles  to  Permeability  of  Medium  in  Magnetic 

Field       .  .  . ,  .  .  .  .241 

Lines  of  Magnetic  Force  .  .  .  .  .  .241 

To  Show  the  Direction  of  the  Lines  of  Magnetic  Force          .  .   242 

To  Trace  the  Lines  of  Force  by  means  of  a  Magnetic  Needle  .  243 
Mapping  the  Lines  of  Magnetic  Force  by  means  of  Iron  Filings  .  243 
Theory  of  Magnetic  Curves  .  .  -  .  .  .  244 

THE    EARTH    A    MAGNET 

The  Earth's  Magnetic  Field  ......  245 

The  Dipping  Needle         .  .  .  .  .  .  245 

Magnetic  Induction  of  the  Earth        .....  246 

Magnetic  Curves  of  the  Earth       .....  246 

MAGNETIC    STRENGTH    OF   FIELD 

Definitions     .  .  .  .  .  .  .  .   247 

Questions  on  Magnetism  .          .    .  _,         .  .  .  .         248 

ELECTROSTATICS 
ELECTRIFICATION 

Electrification  of  Sealing  Wax  and  Glass       ....   248 

Origin  of  Name  Electrification     .....         249 

Electrics  and  Non-electrics    .  .  .  .  .   249 

Electric  Repulsion  ......         249 

Two  Kinds  of  Electrification  .  .  .  .  .251 

Transference  of  Electrification  by  Contact  .  .  .251 


xxii  TABLE  OF  CONTENTS 

PACE 

Opposite  Character  of  Two  Kinds  of  Electrification  .  .251 

Use  of  Terms  Positive  and  Negative        .             .             .             .,  252 

Simultaneous  Production  of  Both  Kinds  of  Electrification     .              .  252 

The  Electrostatic  Series   .             .             .             .             .             .  253 

ELECTRIC    CONDUCTION 

Conductors  and  Non-conductors        .....  253 

Insulators              .          '   ;             •             .             .             .             .  254 

ELECTROSTATIC    INDUCTION 

Electrification  by  Induction  .             .             ...             .              .  255 

Equality  of  Induced  -j-  and  —  Charges  .             .             .             .  256 

The  Electrophorus     .             .             .             ,             „             .             .  256 

The  Bound  Charge           .             .            -.             ,             .         .    ..  257 

THE   ELECTRIC    FIELD 

Electric  Attraction  and  Repulsion  Due  to  the  Medium  Surrounding 

the  Charge           ...             .-            .             ..           .             .  257 

The  Dielectric  and  Electric  Elasticity      .             .             .             .  258 

The  Luminiferous  Ether  a  Dielectric             .             .             .              .  258 

Lines  of  Electric  Force     .             .             .             .                           .  258 

To  Show  the  Effect  of  Surrounding  Conductors  upon  the  Electric 

Field       .  .  .  .  .  .  .  .259 

Electric  Condensers          .             .             .             .             .             C  260 

The  Electric  Field  of  the  Leyden  Jar            '.    ,     .    v            .             .  260 

Energy  of  the  Electric  Field  in  the  Dielectric      .             .             .  261 

Electric  Field  of  a  Hollow  Conductor             ....  262 

Mapping  the  Lines  of  Electric  Force        .         ; "  -.             .             .  264 

Electric  Potential       .             .             .             .             .             .              .  265 

Zero  Potential       .             .                                        .             .             .  267 

Potential  Difference  .             .             .             ,             .             .             .  267 

Electromotive  Force          .             .             .             .           ...  268 

ELECTRIC    QUANTITY 

Definition  of  Unit  Quantity   ......  268 


TABLE  OF  CONTENTS  xxiii 

ELECTRIC    CAPACITY 

PAGE 

Definition  of  Electric  Capacity  .....  269 

Capacity  of  a  Condenser  ......         269 

SPECIFIC   INDUCTIVE   CAPACITY 

Experiment  on  Specific  Inductive  Capacity  of  Paraffin          .  .  270 

Definition  of  Specific  Inductive  Capacity  .  .  «         271 

Relation  of  Specific  Inductive  Capacity  to  Electric  Elasticity  .  272 

ELECTRIC    DISCHARGE 

Discharge  of  Electrification  from  a  Pointed  Conductor  .             .  273 

The  Spark  Discharge       ...  .                      273 

Instantaneous  Character  of  Spark  Discharge              .  .              .  274 

Oscillatory  Character  of  Spark  Discharge            .  .             .         275 

Fall  of  Potential  in  Electric  Conduction          .             .  .  275 

ELECTRIFICATION   OF   THE   EARTH 

The  Earth's  Electric  Field  i            .             .             .  .276 

Electrification  of  the  Air  .  .             .             .             .             .  277 

Electrification  of  Clouds  .             .             .             .             .  .  278 

Protection  from  Lightning  .                          ...  279 

CURRENT   ELECTRICITY 
THE   VOLTAIC   CELL 

Displacement  of  one  Metal  by  Another  in  an  Acid  Solution  .  .  280 

Formation  of  Ions  in  the  Solution  .                                        .280 

Positive  Charges  of  Metallic  Ions       .  .              .              .              .281 

Differences  in  Electrical  Conditions  of  Different  Metals  in  the  Same 

Solution          .             .             .  .  .         281 

Production  of  the  Electric  Current     .  .                           .281 

Construction  of  the  Voltaic  Cell   .  .         282 

PROPERTIES    OF   THE    ELECTRIC    CURRENT 

Magnetic  Field  of  the  Current  .   283 

Direction  of  the  Lines  of  Magnetic  Force  about  u  Current  .         283 


xxiv  TABLE  OF  CONTENTS 


Temperature  Effect  of  Current  .  .  .  284 

Chemical  Effect  of  Current  .  .  .  .  .         284 


MAGNETIC   EFFECTS   OF   THE   CURRENT 

Rotation  of  a  Magnetic  Pole  About  a  Current            .          ;•  .  .  284 

The  Galvanometer            .             .             .  a          .             .             w  286 

The  Solenoid              .             ,            .            .            .            .  .  287 

Magnetic  Field  of  a  Solenoid        .             .                          .             .  287 

The  Electro-magnet  .             ..             .             .          .,  .        *    .  .   287 

Magnetization  by  Means  of  a  Solenoid     .             .             .             ,  288 

The  Electro-magnetic  Telegraph       .             .             .             .  .288 

The  Electric  Bell  .             .          '  .             .             .             .             .  289 

ELECTRO-MAGNETIC   INDUCTION 

Induction  of  Current  by  Moving  Magnet        ....  289 

Induction  of  Current  by  the  Magnetic  Field  of  Another  Current  290 

Primary  and  Secondary  Currents      .             .             ....  .   291 

Potential  Difference  Induced  at  Terminals  of  Secondary  Coil      .  291 

The  Induction  Coil    .             ...             .             .             .  .   292 

Experiments  with  Induction  Coil              .             .             .             .  292 

The  Dynamo  Machine            .             .    '         .            (.             .  .   293 

The  Direct-current  Dynamo         »              ,              .              .              .  294 

Electric  Motors           .......  295 

Experiments  with  the  Dynamo  Machine  and  the  Motor  .             .  297 

The  Transformer       .             .             .             .             .             -.  297 

The  Electro-magnetic  Telephone              .             .             .             .  .  298 

Induction  of  Telephone  Current         .....  298 

Production  of  Sound  Waves  by  Telephone            .             .             .  299 

The  Bell  Telephone  .....  .   299 

Other  Forms  of  Telephone            .             .             .             .  .          .  299 


HEATING    EFFECT   OF    CURRENT 

Work  Done  in  Overcoming  the  Resistance  of  a  Conductor    .  .   300 

Energy  Used  in  Heating  Conductor          ....  300 

Resistance  of  Uniform  Conductor  Proportional  to  its  Length  .  301 


TABLE  OF  CONTENTS  xxv 

ELECTRICAL   UNITS  AND   MEASUREMENTS 

PAGE 

Practical  Units  .             .             .  .             .             .             .301 

The  Volt  .  .        "   .'            .             .  .                                   301 

'i'he  Ohm  .             .             .  .             .             .             .  302 

The  Ampere  .             .            »             .  .             .             .         302 

The  Joule       ...  .  .            .            .            .  302 

The  Watt  .....  .             .             .302 

The  Kilowatt  .            .            „  .             .             .             .  302 

Ohm's  Law  .             .             .             .  .             .             .         302 

Joule's  Law    .  .             .             .  .                          .             .  303 

Problems  .......         304 

PRACTICAL  APPLICATIONS   OF   ENERGY  OF  THE 
CURRENT 

Electric  Lighting        .  .-          .             .             .             .             .  305 

The  Incandescent  Lamp  .  .             .             .             .  .         »         305 

The  Arc  Lamp           .  .             .             .             .             .             .  306 

Efficiency  of  Lamps          .  .             .             .             .         306 

Electric  Welding "     .  .             .             .             ,           •  .             .  306 

The  Electric  Furnace       .  .             .                           .             .         307 

Electric  Heating         .  .             .             .             .             .             .   307 

Loss  of  Energy  in  Electrical  Transmission  .             .             .         307 

CHEMICAL    EFFECTS    OF   THE   CURRENT 

Current  Through  Solutions  Accompanied  by  Chemical  Changes  .  309 

Conduction  of  Current  by  Copper  Sulphate  Solution        .             .  310 

Dissociation  of  Water  by  Current      .         — -»             .              .  .   311 

Electrolysis           .             ..            .             .             .             ...  312 

Theory  of  Electrolysis            .             *    :         .             .             .  .312 

Measurement  of  Current  Strength  by  Means  of  Electrolysis         .  312 

The  Voltameter         .             .           . .             .             .             .  .  3 13 

Electro-chemical  Equivalents        .              .  -"                       .              .  314 

Electrolytic  Polarization        .             .             .             .             .  .  314 

Currents  Due  to  Polarization        .  .          .              .              .              .  315 

Storage  Cells              .             .             .             .             .             .  .315 

Internal  Resistance  of  Cells          .  .  .  .  .316 

Grouping  of  Cells      .              .             .             .                           .  .318 

Problems                ...,,,.  319 


xxvi  TABLE  OF  CONTENTS 

ELECTRIC  RADIATION 
ELECTRIC    WAVES 

PAC.E 

Maxwell's  Theory      .           •  .             .             .             .             .  .  320 

Hertzian  Waves   .             .             .         -    *             .             .             .  321 

Electric  Resonance    .           *.             .             .             .             .  .321 

The  Coherer     '  .             .             .         -   .             .           ..             .  323 

Wireless  Telegraphy              .           •.           i,           -.             .  .  324 

ROENTGEN   RADIATION 

Electric  Discharge  in  Rarefied  Gases  ....  324 

Kathode  Rays      .             .             .             .             .             .             .  325 

Formation  of  Roentgen  Radiation     .             .             .             .  .   325 

Properties  of  Roentgen  Radiation             .....  326 

Problems        .             ...             .             *             .  .   327 


PART    VI 

OPTICS  AND   RADIATION 
DEFINITIONS 

Origin  of  Radiant  Energy    .  .             .             .             .             .  329 

Light       .             .             .             .  .             .             ...          .         329 

Optics            .             .             .  .             .            ..                               329 

Radiation  best  Studied  in  Optics  .             .             .             .         329 

ORIGIN    OF   LIGHT 
Luminous  Bodies       .  ..  .  ....  .  329 

PROPAGATION   OF    LIGHT 

Transmission  by  Optical  Medium     .  .  .  , ,  .  329 

Velocity  of  Light  Propagation      ,  .  .  .  330 

First  Law  of  Light  Propagation         .....  332 

Light  Waves         .......  332 


TABLE  OF  CONTENTS  xxvii 


PAGE 


Wave-front    „  .  .  .  ,  .  .  .332 

Law  of  Decrease  of  Intensity        .....         332 

PHOTOMETRY 

Definitions     ........  333 

The  Rumford  Photometer             .....  333 

The  Bunsen  Photometer         ......  334 

The  Joly  Photometer        ......  334 

Comparison  of  Photometers  ......  335 

To  Test  the  Law  of  Inverse  Squares         ....  335 

Candle  Power  of  a  Lamp       ......  336 

Problems                .......  337 

REFLECTION   OF    LIGHT 

Reflective  Power  of  Various  Bodies  .....  337 

Regular  and  Irregular  Reflection  ....  337 

Effect  of  Polishing  Surface  or  Reflecting  Body          .  .  .  338 

Huyghens'  Construction  for  Advancing  Wave-front         .  .  338 

REFLECTION    FROM    PLANE  SURFACES 

Reflection  from  Plane  Mirror  .....  340 

Virtual  Image  by  Reflection  from  Plane  Mirror  .  .  . "       341 

To  Locate  the  Virtual  Image  of  a  Plane  Mirror         .  .  .   341 

The  Method  of  Rays         .  .  .  .  .344 

Multiple  Reflection  by  a  Mirror          .....  346 

REFLECTION    FROM    CURVED    SURFACES 

Projection  of  a  Wave-front  Reflected  from  a  Curved  Surface  .   346 

Reflection  from  Convex  Spherical  Surfaces           .             .             .  347 

Images  Seen  by  Reflection  from  a  Convex  Surface    .              .  .   347 
Reflection  of  a  Plane  Wave-front  from  a  Convex  Spherical  Surface      347 

Reflection  from  a  Concave  Spherical  Surface                           .  .  348 

Contraction  of  Concave  Wave-front          ....  349 

Focus  of  Concave  Wave -front             .             .             .             .  -35° 

Focal  Length  of  Concave  Mirror  .....  350 

Relation  of  Focal  Length  to  Radius  of  Curvature      .             .  .  350 

Spherical  Aberration         .             .             .             .             .  351 


xxviii  TABLE  OF  CONTENTS 


PAGE 

Real  and  Virtual  Images  in  Concave  Mirrors  .  .  .  351 

Conjugate  Foci     .  .  .  .  .  .         353 

Experiments  with  Concave  Mirror    .  .  .  .  -354 


REFRACTION   OF   LIGHT 

Definition       .             .             .             .             .             .             .  .  355 

Refraction  at  Plane  Surface          .             .             .             .  .         355 

To  Find  the  Relative  Velocities  of  Light  in  Air  and  Glass    .  .  356 

Refractive  Index                .  -           .             .             .             .  .         357 

Angle  of  Refraction  .             .             .             .             .             .  .  358 

REFRACTION  AT  CURVED  SURFACES 

Refraction  of  Spherical  Surface         .   .          .             .             ,  '         .  358 

Lenses       .             .             .             .  .           .             .             .  .         359 

Refraction  by  a  Convex  Lens             ..             .             .         -.    »  .  360 

Refraction  by  Concave  Lenses     .             .             .  .         361 

TOTAL   REFLECTION 

Cause  of  Total  Reflection      .             .             .             .            ,  .361 

Experiments  on  Total  Reflection              .              .             .,  .         362 

REFRACTION   BY  TRIANGULAR   PRISM 

Change  in  Direction  of  Wave  by  Triangular  Prism  .             .  -363 

To  Trace  the  Path  of  a  Ray  through  a  Triangular  Prism  .         364 


DISPERSION    OF  LIGHT 

Dispersion  by  Triangular  Prism        .....  364 

The  Spectrum       .......         365 

Recombination  of  Spectrum  .  .  „  .  .  -365 

Complementary  Colors      .  .  .  .  .  .366 

Color  of  the  Bodies    .......  366 

Dispersion  in  Lenses         ......         367 

Chromatic  Aberration  ......  367 

Achromatic  Lenses  .  .  .  .  „  .368 


TABLE  OF  CONTENTS  xxix 

INTERFERENCE   OF   LIGHT 
INTERFERENCE   BY  REFLECTION 

PAGE 

Newton's  Rings         .......  369 

Comparison  with  Sound  Interference        ....         370 

Theory  of  Interference  .  .  .  .  .  .  371 

Estimation  of  Wave-length  by  Interference          .  .  .374 

Periodic  Character  of  Light  Waves  .....  374 

INTERFERENCE   BY  DIFFRACTION 

Diffraction  by  Narrow  Obstacle         .             .             .  .             •  375 

Measurement  of  Wave-length  by  Diffraction        .  .             .         376 
To  Measure  the  Wave-length  of  Sunlight       ....  378 

The  Diffraction  Grating  .             .             ,             .  .             -378 

The  Grating  Spectrum           .             .             .             .  .             -379 

Measurement  of  Wave-length  by  Diffraction  Grating  .             .         380 

To  Measure  the  Wave-length  of  Sodium  Light           .  .             .381 

RECTILINEAR   PROPAGATION 

Rectilinear  Propagation  due  to  Interference  .  .  .381 

DOUBLE   REFRACTION   AND   POLARIZATION 

Double  Refraction  in  Iceland  Spar   .  .             ..            .             -383 

Double  Refraction  in  Tourmaline             ,  .            .             .384 
Polarization  by  Double  Refraction    .....   384 

Light  Waves  due  to  Transverse  Vibrations  .             .             .         385 

Polarization  of  Hertzian  Waves         .  .             ...             .386 

Polarization  by  Reflection            .  387 

Theory  of  Polarization  by  Reflection  ....  387 

THE   NATURE   OF   LIGHT 

Visible  and  Invisible  Radiation          .  .  .  .  .  389 

Relation  of  Visibility  to  Wave-length  of  Radiation          .  .         389 

Unknown  Nature  of  Roentgen  Radiation  .  390 

The  Becquerel  Radiation  .....         391 

Electro  magnetic  Origin  of  all  Radiation       ....  391 


xxx  TABLE  OF  CONTENTS 

PROPERTIES   OF   THE    ETHER 

PAGF 

Properties  Inferred  from  Nature  of  Radiation  .  .  .   391 

SPECTRUM   ANALYSIS 

Emission  Spectra        .  .  .  .  .  .  392 

Characteristic  Spectra  of  the  Elements     ....         393 

Continuous  Spectra     .......  393 

Radiation  due  to  Atomic  Vibrations         .  .  «  .         393 

Use  of  Spectrum  Analysis      .  .  »  .  .  -394 

The  Spectroscope  ...  .  .  .  .         394 

Absorption  Spectra    .  .  ....  .  .  395 

Absorption  by  Sodium  Vapor        .  .  .  .  -395 

THE   SOLAR    SPECTRUM 

The  Sun's  Spectrum  not  Continuous  .             .             .             .   396 

Fraunhofer's  Lines         .   .             .  .             .             .             .         396 

Theory  of  the  Sun's  Spectrum           .  .             .             .             •  397 

Composition  of  the  Sun    .             .  .             .             .             .         397 

STELLAR   SPECTRA 

Absorption  Spectra  of  the  Stars         .  •  .  .  .  398 

Photographs  of  Stellar  Spectra     .  .  .  ..  .         398 

OPTICAL   INSTRUMENTS 

Two  Kinds  of  Optical  Instruments  .  .  .  .  398 

The  Camera          .  .  ,  - .  .  .         '    ...        399 

The  Projection  Lantern         .  .  .  ,  .  .   400 

The  Eye  ...  .  .  .  .400 

Defects  of  Vision        .  .  .  .  .  .  .  402 

The  Simple  Microscope    .  .  .  .  .  .*         402 

The  Microscope  as  an  Aid  to  Vision  ....  403 

Magnifying  Power  ......         404 

The  Compound  Microscope    .......  405 

The  Telescope      .  ...         406 


TABLE  OF  CONTENTS  xxxi 

i 

PAGE 

Construction  of  a  Microscope  and  a  Telescope          .  .  .  406 

The  Spy  Glass     .......         407 

COLOR   VISION 

Young's  Theory  of  Color  Vision         .....  407 
Color  Blindness    .......         408 

COLOR   PHOTOGRAPHY 

Lippmann's  Process  ......  408 

Ives'  Method  .  .  .  .  .  .409 


PHYSICS 

PART  I 

MECHANICS 

FUNDAMENTAL  DEFINITIONS 

Physics. — Physics  is  the  science  which  treats  of  the 
changes  that  take  place  in  the  physical  universe. 

The  Physical  Universe. — The  physical  universe  is 
that  part  of  the  universe  which  is,  so  far  as  we  know, 
made  up  of  the  two  fundamental  existences,  Matter 
and  Energy. 

Matter. — No  complete  definition  of  matter  is  pos- 
sible. We  may  learn  of  the  properties  of  material 
bodies,  but  the  essential  nature  of  matter  is  entirely 
unknown  to  us.  The  name  is  generally  understood  to 
mean  the  indestructible  substance  of  all  bodies  which 
are  appreciable  by  our  senses. 

Energy. — The  essential  nature  of  energy  is  likewise 
unknown.  We  can  measure  its  quantity,  but  we  know 
nothing  of  its  descriptive  qualities.  It  may  be  pro- 
visionally defined  as  the  capacity  for  doing  work. 

Work. — The  term  work,  as  used  in  Physics,  may  be 
defined  as  the  producing  of  such  changes  in  the  rela- 
tive positions  or  relative  motions  of  material  bodies  as 
would  require  an  effort  on  our  part  to  produce.  Thus 
we  do  work  upon  a  stone  when  we  lift  it  from  the 


2  PHYSICS 

ground  or  when  we  throw  it.  In  the  one  case  we  have 
produced  a  change  in  the  relative  positions  of  the  stone 
and  surrounding  objects;  in  the  other  case  we  have 
changed  the  velocity  of  the  stone  with  reference  to  sur- 
rounding objects. 

An  effort  which  does  not  produce  a  change  in  either 
the  relative  positions  or  the  relative  velocities  of  mate- 
rial bodies  or  the  material  particles  of  which  they  are 
composed  does  not  result  in  work.  Thus  it  may  re- 
quire a  great  effort  to  hold  a  heavy  stone  supported 
above  the  earth,  but  as  long  as  the  stone  is  held  in  a 
fixed  position  relative  to  the  earth,  no  work,  in  the 
physical  sense,  is  done  upon  it. 

Measurement  of  Work. — Work  is  generally  meas- 
ured by  the  energy  expended  in  lifting  a  body  of  known 
weight  through  a  given  vertical  distance  above  the 
earth.  Thus  to  lift  a  pound  weight  one  foot  high  is 
to  do  one  foot-pound  of  work,  and  requires  the  expen- 
diture of  one  foot-pound  of  energy.  To  lift  two  pound 
weights  one  foot  high  or  one  pound  weight  two  feet 
high  is  to  do  two  foot-pounds  of  work. 

MACHINES 

Definition. — A  machine  is  an  instrument  by  which 
energy  is  applied  to  the  performance  of  work. 

The  Lever. 

LABORATORY  EXERCISE  i. — A  uniform  wooden  bar  four  or 
five  feet  long  should  be  so  balanced  on  a  horizontal  axis 
through  its  middle  point  that  it  will  remain  in  equilibrium 
when  inclined  at  any  angle  to  the  horizontal.  It  should  be 
placed  in  front  of  a  wall  or  vertical  board  ruled  in  horizontal 
lines  one  inch  apart,  or  a  yardstick  ruled  in  inches  may  be 
supported  vertically  back  of  each  end  of  the  bar  as  shown 
in  Fig.  i. 

Suspend  a  one-pound  weight  from  one  end  of  the  bar,  and 


MECHANICS  3 

taking  hold  of  the  bar  with  the  hand  turn  it  on  its  axis  until 
the  weight  has  been  raised  one  foot. 

How  much  work  have  you  done  upon  the  weight  ? 

Is  the  amount  of  work  done  upon  the  weight  the  same 
no  matter  where  you  take  hold  of  the  bar  ? 

Suspend  a  pound  weight  near  the  other  end  of  the  bar 
where  it  will  be  raised  by  the  falling  of  the  first  weight  when 
the  bar  is  released. 


FIG.  i. 

In  raising  the  first  weight  work  was  done  upon  it.  By 
virtue  of  this  work,  the  weight  was  raised  into  a  position 
where  it  had  more  energy  than  it  had  before.  This  energy, 
we  have  seen,  may  be  used  in  raising  another  weight  on  the 
other  end  of  the  bar. 

Place  the  second  weight  at  the  same  distance  from  the  axis 
as  the  first  weight.  It  wilt  then  be  raised  as  far  as  the  first 
weight  falls,  and  will  acquire  energy  as  fast  as  the  first 
weight  loses  it.  Will  either  weight  raise  the  other  under 
these  conditions  ? 

State  the  conditions  of  equilibrium  for  two  equal  weights 
on  the  bar. 

Balance  a  one-pound  weight  on  one  side  of  the  axis  by  a 
half-pound  weight  on  the  other  side.  What  of  the  distances 
through  which  the  two  weights  move  when  the  bar  is  turned  ? 
Compare  the  energy  gained  on  one  side  with  the  energy  lost 
on  the  other  side. 

State  the  conditions  of  equilibrium  for  unequal  weights 
on  the  bar : 

(a)  In  terms  of  the  gain  or  loss  of  energy  on  each  side. 


4  PHYSICS 

(b)  In  terms  of  the  products  of  the  weights  into  the  re- 
spective distances  through  which  they  move. 

(c)  In  terms  of  the  products  of  the  weights  into  their  re- 
spective distances  from  the  axis  of  the  bar. 

The  Lever  as  a  Machine. — A  rigid  bar  supported  as 
above  on  an  axis  about  which  it  may  turn  may  be  used 
to  raise  weights  or  to  move  heavy  bodies.  When  so 
used,  it  becomes  a  machine,  and  is  called  a  Lever. 

The  axis  upon  which  the  lever  turns  is  called  the 
Fulcrum. 

The  arm  upon  which  the  weight  is  raised  or  by 
which  the  work  is  done  is  called  the  Work  Arm. 

The  arm  to  which  the  energy  is  applied  to  do  the 
work  is  called  the  Power  Arm. 

Since  both  the  weight  and  the  energy  which  moves 
it  may  act  on  the  same  side  of  the  fulcrum,  the  same 
part  of  the  lever  may  belong  to  both  the  power  arm 
and  the  work  arm. 

Classes  of  Levers. — When  the  lever  has  its  fulcrum 
between  the  power  arm  and  the  work  arm,  it  is  called 
a  lever  of  the  first  class. 

When  the  weight  to  be  raised  or  the  body  to  be 
moved  is  between  the  point  of  application  of  the  energy 
and  the  fulcrum,  it  is  called  a  lever  of  the  second 
class. 

When  the  energy  is  applied  between  the  weight  and 
the  fulcrum,  it  becomes  a  lever  of  the  third  class. 

Make  diagrams  illustrating  the  three  classes  of  levers. 
To  which  class  of  levers  does  the  nut-cracker  belong  ? 
The  common  fire-tongs  ?     The  wheelbarrow  ? 

Most  of  the  movements  of  our  bodies  are  performed 
by  means  of  levers.  Fig.  2  shows  the  bones  of  the 
arm  with  the  biceps  muscle  attached.  To  which  class 


MECHANICS  5 

of  levers  does  the  forearm  belong  when  it  is  being  bent 
upon  the  arm  ? 


FIG.  2. 

Moment. — The  product  of  the  weight  or  power  into 
its  perpendicular  distance  from  the  fulcrum  is  called  its 
Moment. 

State  the  conditions  of  equilibrium  of  a  lever  of  the  first 
class  in  terms  of  the  moments  of  its  power  and  weight. 

Mechanical  Advantage. — We  have  seen  that  no 
work  is  saved  by  the  use  of  a  lever.  The  same  amount 
of  energy  must  be  used  to  do  a  given  quantity  of  work 
with  any  lever.  By  means  of  a  lever,  however,  one 
may  do  work  which  he  could  not  possibly  do  without 
it.  Thus  a  man  who  can  lift  only  two  hundred  pounds 
may  lift  a  thousand  pounds  with  a  lever.  In  this  case 
the  lever  is  said  to  give  him  a  mechanical  advantage 
of  five;  i.e.,  by  means  of  it  he  can  lift  five  times  as 
much  as  he  could  without  it. 

When  a  weight  of  one  pound  on  one  arm  of  a  lever 
balances  a  weight  of  twelve  pounds  on  the  other  arm, 
the  lever  is  said  to  give  the  lighter  weight  a  mechanical 
advantage  of  twelve. 

In  general,  the  ratio  of  the  weight  upon  which  the 


6  PHYSICS 

work  is  done  to  the  weight  doing  the  work  is  called 
the  mechanical  advantage  of  the  lever. 

PROBLEMS. — State  the  mechanical  advantage  of  a  lever  in 
terms  of  the  distances  travelled  by  the  power  and  weight. 

What  is  the  mechanical  advantage  of  a  lever  in  which 
the  work  arm  is  two  feet  long  and  the  power  arm  three  feet 
long? 

The  Fixed  Pulley. 

LABORATORY  EXERCISE  2. — Attach  a  pulley*  to  a  support 
two  or  three  feet  above  the  table  and  suspend  a  pound 
weight  by  a  cord  passed  over  the  pulley  and  held  in  the 
hand.  Pull  on  the  cord  and  raise  the  weight  one  foot. 
Through  what  distance  does  your  hand  move  ?  Is  there  any 
mechanical  advantage  in  a  fixed  pulley  ?  What  weight  must 
be  attached  to  the  string  to  balance  the  pound  weight  ? 
When  the  weights  are  in  equilibrium,  will  one  always  gain 
energy  as  fast  as  the  other  loses  it  ? 

Show  how  the  fixed  pulley  may  be  regarded  as  a  lever. 
To  which  class  of  levers  does  it  belong  ? 

Levers  of  the  Second  and  Third  Classes. 

LABORATORY  EXERCISE  3. — Place  the  fixed  pulley  above 
one  end  of  a  lever  mounted  as  in  Fig.  3.  Attach  one 
end  of  the  cord  to  the  end  of  the  lever,  hang  a  pound 
weight  on  the  other  end  of  the  cord  and  balance  it  by  weights 
suspended  from  the  lever  between  the  cord  and  the  fulcrum. 
When  the  weights  are  in  equilibrium,  turn  the  pulley  until 
the  pound  weight  has  lost  one  foot-pound  of  energy.  How 
much  energy  has  been  gained  by  the  weights  on  the  bar  ? 

State  the  conditions  of  equilibrium  for  a  lever  of  the 
second  class  in  terms  of  the  energy  expended  and  the  work 
accomplished.  Do  the  other  conditions  of  equilibrium  in 
the  lever  of  the  first  class  apply  to  the  lever  of  the  second 
class  ? 

Attach  the  cord  to  the  lever  near  the  fulcrum,  hang  a 
pound  weight  near  the  end  of  the  bar  and  balance  by  weights 
on  the  other  end  of  the  cord.  State  the  conditions  of  equi- 
librium in  a  lever  of  the  third  class. 

*  In  all  of  the  pulleys  used  in  the  experiments  here  given  the  axles 
should  turn  in  their  bearings  with  very  little  friction. 


MECHANICS  7 

Assuming  the  work  to  be  done  in  raising  the  weights  at- 
tached to  the  bar  and  the  energy  to  be  applied  by  means  of 


FIG.  3. 

the  cord,  tell  in  which  of  the  two  classes  of  levers  there  is  a 
mechanical  advantage. 

The  Movable  Pulley. 

LABORATORY  EXERCISE  4. — Suspend  a  weight  from  a  mov- 
able pulley  which  is  supported  by  a  cord  attached  at  one 
end  and  passing  around  the  movable  pulley  is  carried  up- 
ward and  over  a  fixed  pulley,  as  shown  in  Fig.  4.  Bal- 
ance the  movable  pulley  and  weight  by  weights  attached  to 
the  free  end  of  the  cord.  Regarding  the  weight  of  the  mov- 
able pulley  as  a  part  of  the  weight  to  be  raised,  what  is  its 
mechanical  advantage  ? 

Systems  of  Pulleys. — Many  possible  combinations 
of  pulleys  may  be  made.  A  common  method  of  using 
several  pulleys  with  a  single  cord  is  to  mount  a  num- 
ber of  pulleys  side  by  side  in  the  same  frame  so  that 
they  may  all  turn  on  the  same  axle.  Two  sjch  sets 
of  pulleys  are  used  together,  the  one  being  attached  to 


PHYSICS 


the  support  and  the  other  to  the  weight,  and  a  single 
cord  is  passed  around  all  the  pulleys  as  in  Fig.  5.  Such 
an  arrangement  is  known  as  a  block  and  tackle. 


FTG.  4.  FIG.  5. 

Mechanical  Advantage  of  Systems  of  Pulleys. 

LABORATORY  EXERCISE  5.— It  is  said  that  the  mechanical 


MECHANICS  9 

advantage  of  any  system  of  pulleys  using  a  single  cord  is 
numerically  equal  to  the  number  of  parts  of  the  cord  which 
support  the  weight.  Arrange  a  system  of  fixed  and  mov- 
able pulleys  and  test  this  statement.  Give  a  diagram  of  the 
system  used. 

The  Inclined  Plane. — In  raising  or  lowering  heavy 
bodies  they  are  often  wheeled  or  rolled  up  or  down  a 
rigid  plane  surface  inclined  at  an  angle  to  the  hori- 
zontal. Thus,  in  loading  barrels  into  a  wagon  they 
are  frequently  rolled  up  a  plank,  one  end  of  which 
rests  upon  the  ground'  and  one  upon  the  wagon. 
When  used  in  this  way,  the  plank  becomes  a  machine, 
and  is  called  an  inclined  plane. 

LABORATORY  EXERCISE  6. — An  inclined  plane  made  of  a 
smooth  board  is  provided  with  a  fixed  pulley  at  its  upper 


FIG.  6. 


end.  Place  a  loaded  car  or  roller  on  the  inclined  plane,  and 
support  it  by  weights  suspended  from  a  cord  passed  over  the 
fixed  pulley  and  running  parallel  to  the  plane. 

Can  you  support  a  heavy  weight  upon  the  plane  by  a 
lighter  weight  upon  the  cord  ? 

When  the  weights  are  in  equilibrium,  pull  on  the  string  and 
determine  the  vertical  distance  through  which  each  weight 
moves.  Knowing  the  value  of  the  two  weights,  determine 
if  one  gains  energy  at  the  same  rate  that  the  other  loses  it. 

How  much  work  is  required  to  raise  a  five-pound  weight 
one  foot  high  on  an  inclined  plane,  disregarding  the  friction 


io  PHYSICS 

on  the  plane  ?  Will  the  work  be  the  same  on  a  plane  in- 
clined at  any  angle  to  the  horizontal  ?  Prove  your  state- 
ment for  different  inclinations  of  your  plane. 

State  the  conditions  of  equilibrium  for  two  weights,  one 
of  which  is  supported  on  the  plane  and  the  other  on  the 
cord,  in  terms  of  the  gain  or  loss  of  energy  of  each  weight 
when  they  are  moved. 

Prove  that  to  raise  the  heavy  weight  the  height  of  the 
plane  the  light  weight  must  fall  the  length  of  the  plane. 

In  the  case  of  equilibrium,  what  relation  holds  between 
the  two  weights  and  the  height  and  length  of  the  plane  ? 

State  the  mechanical  advantage  of  the  inclined  plane  in 
terms  of  the  height  and  length  of  the  plane. 

If  the  supporting  cord  were  kept  parallel  to  the  base  of 
the  plane,  how  far  would  the  lighter  weight  fall  in  raising  the 
heavy  weight  the  height  of  the  plane  ?  What  would  be  the 
mechanical  advantage  of  an  inclined  plane  used  in  this  way  ? 

Modifications  of  Lever,  Pulley,  and  Inclined  Plane. 

— Many  modifications  of  the  lever  and  pulley  and  in- 
clined plane  are  used  in  mechanical  work.  Some  of 
the  best-known  forms  are  the  Wheel  and  Axle,  Wind- 
lass, Capstan,  and  Screw. 


FIG.  7. 

The  Wheel  and  Axle. — The  wheel  and  axle  consists 
of  two  fixed  pulleys  rigidly  attached  to  each  other  and 
turning  upon  the  same  axis.  The  larger  of  these  is 


MECHANICS  ii 

called  the  wheel,  and  the  smaller,  which  is  generally  in 
the  form  of  a  cylinder,  is  called  the  axle.  The  weight 
to  be  raised  is  attached  to  a  cord  which  is  wound  up  on 
the  axle  by  unwinding  another  cord  from  the  wheel. 

State  the  mechanical  advantage  of  the  wheel  and  axle  in 
terms  of  the  radii  of  the  two  pulleys. 

The  Windlass. — The  windlass  is  an  arrangement 
similar  to  the  wheel  and  axle,  in  which  the  wheel  is 
replaced  by  a  crank,  or  by  spokes  for  turning  by  hand. 
The  Capstan  is  a  form  of  the  same  machine  frequently 
used  on  shipboard.  The  cylinder  around  which  the 
cord  is  wound  is  vertical,  instead  of  horizontal,  and  is 
generally  turned  by  levers  called  capstan  bars  which 
are  thrust  into  holes  made  for  them  in  the  cylinder. 

The  Screw.  —  The  screw  is  a  machine  frequently 
used  for  raising  heavy  weights  or  for  exerting  great 
pressures.  It  is  equivalent  to  a  long  inclined  plane 
wound  around  a  cylinder.  The  power  is  frequently 
applied  to  a  long  lever  attached  to  the  screw.  The 
mechanical  advantage  of  the  screw  is  theoretically  the 
same  as  in  other  machines,  that  is,  the  ratio  of  the  dis- 
tance travelled  by  the  power  to  the  distance  through 
which  the  weight  is  moved.  In  practice  the  friction  is 
considerable,  and  the  mechanical  advantage  is  always 
less  than  its  theoretical  value. 

The  Pitch  of  a  screw  is  the  distance  between  two 
contiguous  threads,  and  is,  accordingly,  the  distance 
travelled  by  the  weight  for  each  revolution  of  the 
screw. 

POWER 

Definition. — The  Power  of  a  machine  is  the  rate  at 
which  it  is  capable  of  doing  work.  The  unit  of  power 


12  PHYSICS 

in  most  common  use  in  our  country  (though  another 
unit  to  be  described  later  !s  coming  into  general  use) 
is  called  the  Horse-power.  It  is  the  rate  of  doing 
work  equivalent  to  33,000  foot-pounds  per  minute. 
Thus  a  machine  of  two  horse-power  is  capable  of  doing 
1 100  foot-pounds  of  work  per  second.  Steam  engines 
are  usually  rated  in  horse-powers. 

EFFICIENCY 

Definition. — In  every  machine  some  of  the  energy  is 
used  in  doing  useless  work  against  friction  or  other 
resistances.  The  ratio  of  the  useful  work  done  by  the 
machine  to  the  total  work  done  upon  it  is  called  the 
efficiency  of  the  machine. 

PROBLEMS. — If  a  weight  of  10  Ibs.  must  be  suspended 
upon  one  side  of  a  fixed  pulley  to  just  raise  a  weight  of  8 
Ibs.  on  the  other  side,  the  efficiency  of  the  pulley  is  .8,  or 
80  per  cent. 

If  one  fourth  of  the  work  done  upon  a  screw  is  used  in 
overcoming  the  friction,  what  is  the  percentage  of  efficiency 
of  the  screw  ? 

GEARING 

Use  of  Gearing. — It  is  often  convenient  in  practice 
to  transmit  power  from  one  shaft  to  another.  This  is 
accomplished  by  means  of  belting,  chain  gearing,  cog 
gearing,  and  the  like. 

PROBLEMS. — In  the  cog  gearing  shown  in  Fig.  8  the  smaller 
wheel  has  16  cogs  and  the  larger  46.  What  is  the  me- 
chanical advantage  of  power  applied  to  the  axle  of  the 
smaller  wheel  ? 

If  the  crank-arm  attached  to  the  smaller  wheel  is  16  inches 
long  and  the  axle  of  the  larger  wheel  is  4  inches  in  diameter, 
what  is  the  mechanical  advantage  of  the  combination  when 
used  to  raise  a  weight  by  winding  a  cord  on  the  axle  of  the 
larger  wheel  ? 

A  machine  is  driven  by  a  belt  from  a  power-shaft  making 


MECHANICS 


three  revolutions  a  second.  The  belt  wheel  on  the  power 
shaft  is  two  feet  in  diameter 
and  that  on  the  driving  shaft 
of  the  machine  is  eight  inches 
in  diameter;  how  many  revo- 
lutions a  second  does  the  driv- 
ing shaft  make  ? 

The  front  sprocket-wheel  of 
a  bicycle  has  30  teeth  and  the 
rear  sprocket  has  12.  If  the 
wheels  are  28  inches  in  diam- 
eter, how  far  does  the  bicycle 
travel  for  one  revolution  of 
the  pedal  cranks  ? 

The  ' '  gear  "  of  a  bicycle  is 
expressed  in  terms  of  the  diam- 
eter   in     inches    of    a    wheel 
which    would  travel  as   far  in 
one  revolution    as  the   geared 
bicycle  travels   in  one  revolu- 
tion of  the  pedal  cranks.    Thus 
a    bicycle    having    a    28-inch 
driving  wheel,  a  front  sprocket 
with  24  teeth  and  a  rear  sprock- 
et of  8  teeth  is  geared  so  that  FlG-  8- 
it    is  equivalent    to    an  ungeared,  or    "ordinary,"    bicycle 
having  a  driving  wheel  84  inches  in  diameter,  and  is  known 
as  an  84-gear  wheel. 

What  is  the  gear  of  the  bicycle  described  in  the  preceding 
problem  ? 

CENTER   OF   GRAVITY 

Definition. — In  our  experiments  with  the  lever,  the 
bar  was  so  balanced  upon  a  pivot  that  it  would  remain 
at  rest  when  turned  into  any  position.  It  is  plain  that 
if  the  pivot  had  been  at  one  end  of  the  bar,  the  bar 
would  have  remained  at  rest  only  in  a  vertical  position. 
If  the  pivot  were  at  a  point  near  one  end,  the  bar  could 
be  balanced  in  a  horizontal  position  only  by  means  of 


i4  PHYSICS 

a  weight  attached  to  its  short  end.  The  bar  accord- 
ingly has  a  moment,  and  since  a  lever  can  be  in  equi- 
librium only  when  the  moments  of  the  weights  on 
opposite  sides  of  the  fulcrum  are  equal  to  each  other, 
the  moment  of  the  weight  attached  to  the  short  end  of 
the  bar  must  equal  the  moment  which  the  bar  itself  has 
on  the  other  side  of  the  fulcrum.  The  point  in  the  bar 
about  which  its  weight  moments  on  opposite  sides  are 
always  equal  is  generally  called  the  Center  of  Gravity 
or  the  Center  of  Mass  of  the  bar.  Neither  of  these 
terms  expresses  the  true  meaning  of  the  position  of  the 
point,  since  in  an  irregular  body  the  weights  on  oppo- 
site sides  of  the  center  of  gravity  may  be  very  unequal. 
To  Find  the  Center  of  Gravity  of  an  Irregular 

Solid. 

LABORATORY  EXERCISE  7. — An  irregular  board  two  or  three 
feet  long  and  of  uniform  thickness  has  a  number  of  small 
holes  bored  straight  through  it.  A  stiff  wire  or  knitting- 
needle  is  driven  horizontally  into  a  rigid  support,  and  the 
board  is  suspended  by  slipping  one  of  the  holes  over  this 
pivot.  When  the  board  comes  to  rest,  the  weight  moments 
on  opposite  sides  of  a  vertical  line  through  the  pivot  must 
be  equal,  hence  the  center  of  gravity  must  be  in  this  vertical 
line.  By  means  of  a  plumb  line  made  by  attaching  a  bullet 
or  other  heavy  body  to  a  thread,  mark  on  the  board  the 
vertical  line  through  the  pivot. 

Place  another  hole  on  the  pivot  and  repeat  the  operation. 
The  two  lines  should  cross  at  a  point  opposite  the  center  of 
gravity  of  the  board.  Do  the  lines  drawn  from  all  the  holes 
cross  at  the  same  point  ? 

If  there  is  not  a  hole  through  the  center  of  gravity,  bore 
one  and  place  this  hole  on  the  pivot.  Are  the  weight 
moments  on  opposite  sides  of  this  hole  equal  with  the  board 
turned  in  any  position  ? 

To  Find  the  Weight  Moment  of  a  Bar  Supported 
from  a  Point  Outside  its  Center  of  Gravity. 

LABORATORY  EXERCISE  8. — Select  a  wooden  bar  two  01 


MECHANICS  15 

three  teet  long,  preferably  not  of  uniform  size,  weigh  it  on 
the  platform  scales,  and  determine  and  mark  the  position  of 
its  center  of  gravity.  (The  piece  of  board  used  for  the 
former  experiment  may  also  be  used  for  this  one.)  Suspend 
the  bar  from  a  pivot,  at  some  distance  from  its  center  of 
gravity.  Attach  a  weight  equal  to  the  weight  of  the  bar  in 
such  a  position  on  the  bar  that  the  bar  will  remain  in  equi- 
librium in  a  horizontal  position.  Measure  the  distances 
from, the  pivot  to  the  suspended  weight  and  to  the  center  of 
gravity  of  the  bar.  How  do  these  distances  compare  ? 

Support  the  bar  at  another  distance  from  its  center  of 
gravity,  and  measure  off  the  distance  from  the  pivot  at  which 
the  weight  must  be  attached  in  order  to  produce  equilibrium 
in  a  horizontal  position.  Attach  the  weight  and  see  if  your 
conclusion  is  correct. 

Define  the  moment  of  a  lever  in  terms  of  its  weight  and 
the  distance  between  its  center  of  gravity  and  the  fulcrum. 

A  bar  weighing  10  pounds  is  suspended  from  a  pivot  three 
feet  from  its  center  of  gravity;  what  is  its  moment  ?  What 
work  must  be  done  upon  the  bar  to  raise  its  center  of  gravity 
two  feet  ?  How  does  this  compare  with  the  work  which 
must  be  done  to  raise  the  whole  bar  two  feet  ? 

A  lever  weighing  20  pounds  is  balanced  by  a  weight  of 
5  pounds  placed  4  feet  from  the  fulcrum ;  how  far  is  the  ful- 
crum from  the  center  of  gravity  of  the  lever  ? 


STABILITY 

Conditions  of  Equilibrium. — We  have  seen  that  the 
weight  moments  of  a  body  are  always  equal  on  oppo- 
site sides  of  its  center  of  gravity,  hence  that  when  the 
center  of  gravity  is  supported  the  body  is  in  equilibrium. 

Stable  and  Unstable  Equilibrium. — When  a  body 
is  so  supported  that  when  disturbed  it  tends  to  return 
to  its  former  position  of  rest  the  body  is  said  to  be  in 
Stable  Equilibrium.  If  a  slight  disturbance  causes  it 
to  seek  a  new  position  of  rest,  it  is  said  to  be  in 
Unstable  Equilibrium. 


1 6  PHYSICS 

Neutral  Equilibrium. — A  body  supported  on  a  pivot 
through  its  center  of  gravity,  or  a  homogeneous  sphere 
resting  on  a  level  surface,  is  said  to  be  in  Neutral 
Equilibrium,  because  it  remains  at  rest  equally  well  in 
any  position  into  which  it  may  be  turned. 

Examples. — A  body  supported  on  a  pivot  directly 
above  its  center  of  gravity  is  in  stable  equilibrium,  since 
when  it  is  turned  into  any  other  position  the  moment 
of  the  body  will  cause  its  center  of  gravity  to  fall  back 
to  its  original  position.  If  the  same  body  be  balanced 
with  its  center  of  gravity  directly  above  the  pivot,  it 
may  remain  at  rest;  but  if  disturbed,  its  center  of 
gravity  will  fall  to  the  stable  position  below  the  pivot. 

If  a  vertical  line  through  the  center  of  gravity  falls 
outside  of  the  support  of  the  body,  the  body  will  not 
be  in  equilibrium  unless  held  in  this  position  by  other 
bodies. 

Why  can  you  not  stand  on  one  foot  with  its  side 
against  the  wall  of  the  room  ? 

Measure  of  Stability. — The  stability  of  any  body 
resting  on  a  surface  may  be  estimated  from  the  amount 
of  work  required  to  overturn  the  body. 

PROBLEMS. — A  homogeneous  cube  four  feet  on  each  edge 
is  resting  on  one  face  on  a  horizontal  surface;  how  high 
must  its  center  of  gravity  be  raised  before  the  cube  can  be 
overturned  ?  If  the  cube  weighs  ten  pounds,  how  much 
work  must  be  done  to  overturn  it  ? 

A  brick  measuring  8  by  4  by  2%  inches  weighs  5  pounds. 
When  resting  on  a  level  surface,  how  much  work  is  required 
to  overturn  it  from  each  of  its  faces  ? 

A  load  of  hay  and  wagon  weighs  two  tons.  If  the  wagon 
wheels  are  four  feet  apart  and  the  center  of  gravity  of  the 
load  is  six  feet  high,  how  much  work  is  required  to  overturn 
it  on  level  ground  ? 


MECHANICS 


THE   PENDULUM 

Energy  of  a  Swinging  Pendulum. 

LABORATORY  EXERCISE  9. — Prepare  a  pendulum  by  attach- 
ing a  thread  or  soft  cord  three  or  four  feet  long  to  a  heavy 


FIG.  9. 

lead  or  iron  ball.  Attach  the  other  end  of  the  thread  to  a 
clamp  or  a  long  nail  driven  into  the  wall  so  that  the  pendu- 
lum will  swing  only  an  inch  or  two  from  a  vertical  wall. 
Rule  the  space  back  of  the  pendulum  in  horizontal  lines  at 
equal  distances  apart. 


1 8  PHYSICS 

Draw  the  ball  to  one  side  so  that  it  shall  be  at  the  same 
height  as  one  of  the  lines,  and  release  it  so  that  it  will  swing 
parallel  to  the  wall.  Note  the  height  to  which  it  rises  on 
the  other  side  of  its  arc. 

Repeat  several  times,  raising  the  pendulum  to  a  different 
height  each  time. 

Does  the  pendulum  acquire  sufficient  energy  in  falling 
through  one  half  its  arc  to  raise  it  again  to  the  same  vertical 
height  from  which  it  has  fallen  ? 

Drive  a  knitting-needle  or  long  nail  into  the  wall  directly 
below  the  point  of  support  of  the  pendulum,  and  at  a  dis- 
tance of  a  foot  or  more  above  the  pendulum  ball.  Draw  the 
ball  to  one  side  as  before,  and  let  it  swing  so  that  the  thread 
will  strike  the  knitting-needle  just  as  the  ball  reaches  its 
lowest  point.  It  will  now  swing  upward  through  a  different 
arc  from  the  one  through  which  it  has  fallen.  Does  it  rise 
to  the  same  height  as  before  ? 

Does  the  energy  acquired  by  a  pendulum  in  falling  through 
one  half  of  its  arc  depend  upon  the  length  of  the  arc,  or  upon 
the  vertical  height  through  which  it  falls  ? 

State  the  same  proposition  with  reference  to  a  ball  rolling 
down  an  inclined  plane. 

Potential  and  Kinetic  Energy  of  the  Pendulum. — 

In  our  previous  experiments  we  have  found  that  the 
energy  which  a  body  has  may  depend  upon  its  vertical 
height  above  the  earth,  or  above  any  horizontal  plane 
to  which  its  energy  is  referred.  We  now  see  that  the 
pendulum  ball  when  at  its  lowest  point  has  energy 
sufficient  to  raise  it  again  to  the  height  from  which  it 
fell  in  acquiring  this  energy.  A  moving  body  may 
accordingly  have  energy  which  is  not  due  to  its  posi- 
tion with  reference  to  other  bodies. 

The  energy  which  a  body  has  on  account  of  its  posi- 
tion is  called  Potential  Energy. 

That  part  of  the  energy  of  a  moving  body  which  is 
not  due  to  its  position  is  called  Kinetic  Energy. 


MECHANICS  19 

When  the  pendulum  ball  is  at  the  lowest  point  of 
its  arc,  its  energy,  considered  as  a  pendulum,  is  all 
kinetic.  It  may  still  have  potential  energy  on  account 
of  its  height  above  the  earth,  but  this  energy  cannot 
be  changed  into  work  so  long  as  it  remains  attached 
to  the  support. 

When  the  ball  is  at  the  end  of  its  swing  it  stops  for 
an  instant  before  turning  back.  At  this  instant  its 
energy  is  all  potential.  Since  its  kinetic  energy  at  the 
lowest  point  of  its  arc  is  sufficient  to  give  it  again  as 
much  potential  energy  as  it  had  at  the  highest  point, 
these  two  quantities  of  energy  must  be  equivalent  to 
each  other.  When  it  is  falling,  it  is  losing  potential 
energy  and  gaining  kinetic.  When  it  is  rising,  it  is 
losing  kinetic  energy  and  gaining  potential.  When 
the  one  kind  has  changed  entirely  to  the  other  kind, 
the  total  quantity  of  energy  is  still  the  same.  When 
it  loses  one  kind  of  energy,  the  pendulum  ball  must 
accordingly  gain  the  other  kind  at  the  same  rate.  If 
it  gave  off  no  energy  to  other  bodies,  its  total  energy 
would  remain  forever  the  same,  though  constantly 
changing  from  one  kind  to  the  other.  In  practice,  it 
does  work  in  setting  the  air  around  it  in  motion,  and 
in  setting  up  vibrations  in  its  support,  which  can  never 
be  absolutely  rigid,  and  hence  its  energy  is  slowly 
given  off  to  other  bodies,  so  that  the  energy  of  each 
succeeding  vibration  is  slightly  less  than  that  of  the 
preceding  one.  If  the  ball  is  very  heavy  and  the 
thread  very  flexible,  the  rate  of  decrease  is  small  and 
cannot  be  perceived  in  a  single  vibration.  It  is  believed 
that  no  body  which  has  energy  can  lose  it  except  by 
giving  it  off  to  some  other  body. 


20  PHYSICS 

Isochronism  of  the  Pendulum. 

LABORATORY  EXERCISE  10. — Suspend  a  heavy  pendulum 
two  or  three  feet  long  in  front  of  a  plumb  line  or  vertical 
mark  on  the  wall,*  and  find  its  time  of  vibration  as  follows: 

Set  the  pendulum  swinging  through  an  arc  of  only  two  or 
three  inches,  and  placing  the  eye  in  a  line  with  the  vertical 
mark  and  the  pendulum  when  at  rest,  note  with  a  watch  or 
clock  provided  with  a  second-hand  the  exact  instant  of  the 
transit  of  the  pendulum  ball  across  this  mark.  Record  this 
time  to  the  nearest  half-second,  and  count  fifty  successive 
transits  of  the  pendulum  ball  in  the  same  direction,  noting 
accurately  the  time  of  the  fiftieth.  This  can  be  done  more 
accurately  if  one  observer  will  count  aloud  the  transits, 
signalling  the  time  of  each  by  tapping  on  the  table  with  a 
pencil,  while  another  observer  reads  the  time  from  the  clock. 

The  interval  between  the  first  and  the  fiftieth  transit 
divided  by  forty-nine  will  give  the  time  of  one  complete 
vibration  of  the  pendulum. 

Make  five  determinations  of  this  time  of  vibration,  using 
arcs  of  nearly  the  same  length.  What  is  the  average  time 
of  vibration  from  the  five  sets  ?  What  is  the  greatest  varia- 
tion from  this  time  in  any  set  ? 

Make  five  determinations  of  the  time  of  vibration  with  the 
pendulum  swinging  through  an  arc  of  a  foot  or  more. 

Does  the  pendulum  swing  more  quickly  through  a  long, 
or  a  short  arc  ? 

Is  the  time  of  vibration  constant  for  small  arcs  ?  What 
use  is  made  of  this  property  of  the  pendulum  ? 

Relation  of  Time  of  Vibration  to  Length  of  Pendu- 
lum. 

LABORATORY  EXERCISE  n. — Prepare  three  pendulums 
respectively  36,  25,  and  16  inches  long,  measuring  from  the 
point  where  the  thread  is  clamped  to  the  support  to  the 
center  of  the  ball,  and  find  their  times  of  vibration  as  before. 

*  Care  should  be  taken  that  the  thread  is  held  tightly  exactly  at  the 
point  of  suspension,  and  that  it  does  not  touch  anything  below  this  point. 
A  good  method  of  suspension  is  to  draw  the  thread  through  a  vertical 
hole  in  the  support  and  fasten  it  by  a  plug  driven  in  from  below  and  cut 
off  flush  with  the  support. 


MECHANICS  21 

Test  the  statement,  "The  times  of  vibration  of  different 
pendulums  are  related  as  the  square  roots  of  their  lengths." 
How  long  must  a  pendulum  be  made  in  order  to  vibrate 
in  half  the  time  of  a  pendulum  36  inches  long  ?  To  vibrate 
in  one  third  the  time  ? 

Relation  of  Time  of  Vibration  to  Weight  and 
Material  of  Pendulum. 

LABORATORY  EXERCISE  12. — Using  pendulums  of  the  same 
length  but  with  balls  of  different  material,  find  if  the  time 
of  vibration  depends  upon  the  weight  or  material  of  the 
pendulum,  or  only  upon  its  length.  Describe  the  pendulums 
used,  and  give  their  times  of  vibration. 

The  Seconds  Pendulum. — The  Seconds  Pendulum  is 
a  pendulum  of  such  length  that  it  swings  once  across 
its  arc  in  one  second,  and  accordingly  makes  one  com- 
plete vibration  in  two  seconds.  Such  a  pendulum  used 
in  a  clock  will  beat  seconds,. 

The  length  of  the  seconds  pendulum  is  different  upon 
different  parts  of  the  earth.  In  the  latitude  of  the 
United  States  and  at  sea  level  it  is  about  39. 13  inches 
or  99.38  centimeters. 

What  is  the  length  of  the  clock  pendulum  which  beats 
half-seconds  ? 

Simple  and  Compound  Pendulums. — In  the  pendu- 
lums used  in  the  preceding  experiments  most  of  the 
weight  has  been  concentrated  in  the  ball  at  the  end  of 
the  thread.  In  the  ideal  Simple  Pendulum  the  weight 
is  regarded  as  being  all  concentrated  at  the  center  of 
the  ball.  When  the  weight  is  not  all  concentrated  at 
a  single  point,  but  is  distributed  to  different  parts  of  the 
pendulum,  the  pendulum  is  said  to  be  a  Compound 
Pendulum.  The  time  of  vibration  of  a  compound 
pendulum  depends  not  upon  its  apparent  length,  but 
upon  the  distribution  of  its  weight. 


22 


PHYSICS 


To  Find  the  Equivalent  Length  of  a  Compound 
Pendulum. 

LABORATORY  EXERCISE  13. — A  piece  of  board  two  or  three 
feet  long  and  wider  at  one  end 
than  at  the  other  should  have  two 
small  holes  bored  straight  through 
it  at  equal  distances  from  the  two 
ends.  By  placing  these  holes  over 
a  knitting-needle  driven  horizon- 
tally into  a  support  the  board  can 
be  made  to  swing  as  a  compound 
pendulum. 

Determine  the  time  of  vibration 
of  the  board  when  suspended  from 
each  end. 

Find  the  length  of  a  simple  pen- 
dulum which  will  vibrate  in  the 
same  time  as  the  board  in  each 
case.  (Attach  the  thread  of  the 
simple  pendulum  to  the  knitting- 
needle,  and  adjust  its  length  until 
the  two  pendulums  will  swing  in 
unison.) 

Centre  of  Suspension  of  a 
Pendulum. —  The  position  of 
the  axis  about  which  a  peiv- 
dulum  swings  is  called  its  Center 
of  Suspension.  The  position 
of  the  knitting-needle  may  be 

taken  as    the  center  of  suspension  of  the  compound 

pendulum. 

Centre  of  Oscillation  of  a  Pendulum. — The  point  in 

a  compound  pendulum  at  which  its  weight  might  all 

be  concentrated  without  changing  its  time  of  vibration 

is  called  the  Center  of  Oscillation  of  the   pendulum. 

This  point  is  found  by  means  of  the  comparison  with 

the  equivalent  simple  pendulum. 


FIG.  10. 


MECHANICS  23 

Mark  the  center  of  oscillation  of  the  board  pendulum  for 
each  center  of  suspension.  Does  either  of  the  centers  of 
oscillation  correspond  with  the  center  of  gravity  ? 

Length  of  a  Compound  Pendulum. — The  length  of 
a  compound  pendulum  is  regarded  as  the  same  as  the 
length  of  the  equivalent  simple  pendulum.  It  is 
accordingly  the  distance  from  the  center  of  suspension 
to  the  center  of  oscillation. 

PROBLEMS. — Is  the  length  of  the  compound  pendulum  the 
same  for  different  centers  of  suspension  ? 

Bore  a  hole  through  one  of  the  centers  of  oscillation  of 
the  pendulum,  and  use  this  point  as  a  center  of  suspension. 
How  is  the  time  of  vibration  of  a  compound  pendulum 
affected  by  changing  its  suspension  to  its  center  of  oscilla- 
tion ?  Are  the  centers  of  suspension  and  of  oscillation 
interchangeable  in  the  same  pendulum  ? 

A  pendulum  is  made  of  a  long  bar  provided  with  two  axes 
so  placed  that  it  makes  one  complete  vibration  in  two 
seconds  when  suspended  from  either  axis.  How  far  apart 
are  the  axes  ? 

Persistence  of  Plane  of  Vibration  of  a  Pendulum. 

LABORATORY  EXERCISE  14. — Make  a  pendulum  by  attach- 
ing a  heavy  weight  to  a  wire  and  suspend  it  from  a  support 
which  can  be  rotated  around  a  vertical  axis.  Set  the  pen- 
dulum swinging  and  turn  the  support  around.  Does  the 
plane  of  vibration  of  the  pendulum  rotate  with  the  pendu- 
lum ? 

Drive  a  knitting-needle  straight  into  the  end  of  a  round 
stick,  as  a  piece  of  broom-handle.  Lay  the  stick  upon  the 
table  and  holding  it  down  with  the  hand,  set  the  needle 
vibrating  through  as  large  an  arc  as  possible,  and  roll  the 
stick  along  the  table.  The  needle  is  thus  made  to  rotate; 
does  its  plane  of  vibration  also  rotate  ? 

Foucault's  Pendulum  Experiment. — In  1851,  Fou- 
cault,  a  French  physicist,  used  this  property  of  the 
pendulum  to  show  the  rotation  of  the  earth.  It  is 
plain  that  a  pendulum  set  swinging  in  a  given  meridian 


24  PHYSICS 

at  the  Equator  would  continue  to  swing  in  that 
meridian  during  an  entire  rotation  of  the  earth.  A 
pendulum  set  swinging  in  a  given  meridian  at  the  Pole 
would  continue  to  swing  in  its  original  plane,  while  the 
meridian  would  swing  completely  around  in  twenty-four 
hours.  To  an  observer  at  the  Pole,  it  would  seem  that 
the  plane  of  vibration  of  the  pendulum  had  made  a 
complete  rotation  in  that  time.  At  any  position 
between  the  Equator  and  the  Pole,  the  plane  of  vibra- 
tion of  the  pendulum  will  appear  to  make  a  partial 
rotation  in  twenty-four  hours.  At  a  latitude  of  40°  this 
apparent  rotation  is  nearly  10°  an  hour,  and  may  be 
easily  shown  with  a  long  and  heavy  pendulum.* 

GRAVITATION 

Definition. — We  have  seen  that  all  bodies  acquire 
potential  energy  as  they  are  raised  above  the  earth „ 
and  that  when  unsupported  they  fall  to  the  earth., 
Likewise,  bodies  resting  upon  the  earth  exert  a  pressure 
upon  objects  beneath  them.  The  cause  of  this  pressure 
is  entirely  unknown  to  us.  It  has  been  named  the 
Gravitation  Pressure,  or  the  Force  or  Attraction  of 
Gravitation.  The  weight  of  a  body  is  the  measure  of 
the  gravitation  pressure  upon  it.  A  falling  body  is 
said  to  acquire  its  kinetic  energy  from  the  work  done 
upon  it  by  gravitation. 

*  For  this  purpose  a  pendulum  weighing  several  pounds  should  be 
suspended  by  a  flexible  wire  from  the  ceiling  or  the  highest  support 
attainable.  Foucault's  original  pendulum  was  200  feet  long,  but  a  pen- 
dulum le  feet  long  will  swing  long  enough  to  show  the  phenomenon. 
The  pendulum  ball  should  be  pulled  to  one  side  a  foot  or  more,  and 
should  b,e  held  by  a  loop  of  thread  fastened  to  a  rigid  support.  When 
everything  is  at  rest,  the  thread  should  be  burned  to  release  the  pen- 
dulum. It  should  swing  just  above  a  table  or  a  level  board  on  which 
its  original  direction  of  vibration  should  be  ca^refqlly  marked. 


MECHANICS  25 

Nature  of  Gravitation  Unknown. — The  pendulum 
swings  to  the  lowest  point  of  its  arc  under  the  influence 
of  gravitation.  In  falling  through  one  half  its  arc 
gravitation  does  work  upon  it,  and  its  kinetic  energy 
is  a  measure  of  this  work.  In  rising  through  the  other 
half  of  its  arc  this  kinetic  energy  is  expended  in  doing 
work  against  gravitation.  At  its  highest  point  it  has 
only  the  potential  energy  due  to  gravitation.  Since 
we  do  not  known  the  nature  of  gravitation,  we  cannot 
know  in  what  form  this  potential  energy  exists,  but  it 
is  believed  to  be  due  to  some  kind  of  pressure  exerted 
by  an  invisible,  elastic  medium  which  surrounds  the 
earth  and  all  bodies,  and  which  is  called  the  Ether. 

Gravitation  and  Time  of  Vibration  of  a  Pendulum. 

LABORATORY  EXERCISE  15. — Suspend  a  pendulum  made  of 
an  iron  ball,  and  determine  as  before  its  time  of  vibration 
through  a  very  small  arc.  Place  a  bar  magnet  with  one  of 
its  ends  just  below  the  ball  when  at  its  lowest  point,  and 
determine  its  time  of  vibration  again  through  a  small  arc. 
The  pull  of  the  magnet  upon  the  ball  affects  the  time  of 
vibration  of  the  pendulum  somewhat  as  would  an  increase 
of  gravitation. 

How  would  an  increase  of  gravitation  affect  the  time' of 
vibration  of  a  pendulum  ? 

The  weight  of  bodies  on  the  earth  is  greater  near  the  poles 
than  near  the  Equator;  in  which  place  would  the  time  of 
vibration  of  a  given  pendulum  be  less  ? 

Attach  a  piece  of  light  elastic  cord  to  the  same  pendulum 
and,  stretching  it  downward  slightly,  determine  the  time  of 
vibration  of  the  pendulum.  Repeat,  stretching  the  cord 
more.  Explain  the  phenomenon  which  you  have  observed. 

Light  and  Heavy  Bodies  Fall  with  Same  Velocity. 

— Since  an  increase  of  gravitation  shortens  the  time  of 
vibration  of  a  pendulum,  it  must  increase  the  velocity 
of  the  falling  pendulum.  Hence  if  gravitation  were 
increased  bodies  would  fall  toward  the  earth  more 


26  PHYSICS 

rapidly.  But  we  saw  from  experiments  in  Exercise  12 
that  all  pendulums  of  the  same  length  have  the  same 
time  of  vibration,  regardless  of  their  weight  or 
material.  This  fact  led  Galileo  to  the  conclusion  that 
light  and  heavy  bodies  fall  with  the  same  velocity 
(though  Aristotle  had  taught  otherwise),  and  he  tested 
his  conclusion  by  dropping  light  and  heavy  balls  from 
the  top  of  the  leaning  tower  in  Pisa. 

The  "  Guinea  and  Feather  Tube." 

LABORATORY  EXERCISE  16. — Exhaust  the  air  from  a 
"  Guinea  and  Feather  Tube,"  *  and  see  if  light  and  heavy 
bodies  fall  with  the  same  velocity  when  not  retarded  by  the 
air. 

MASS 

Potential  Energy  of  a  Body  Proportional  to  its 
Weight. — We  have  defined  weight  as  the  measure  of 
gravitation  upon  a  body,  hence  the  gravitation  pressure 
must  be  greater  upon  a  heavy  body  than  upon  a  light 
one.  Since  the  heavy  body  does  not  fall  faster  than 
the  light  one,  it  must  require  more  work  on  the  part 
of  gravitation  to  move  the  heavier  body.  In  the  same 
manner,  it  requires  the  expenditure  of  more  energy  to 
raise  the  heavier  body  to  a  given  height  against  gravi- 

*  A  modification  of  the  Guinea  and  Feather  Tube  used  in  early  ex- 
periments on  falling  bodies  is  made  as  follows:  A  glass  tube  half  an 
inch  or  more  in  internal  diameter  and  about  three  feet  long  is  sealed  off 
smoothly  at  one  end  by  heating  in  a  flame.  A  small  shot  or  other  heavy 
body  and  a  piece  of  light  paper  are  introduced  into  the  tube,  which 
should  be  carefully  dried,  and  the  tube  is  then  heated  in  a  flame  near 
the  other  end  and  drawn  down  to  a  small  neck.  It  is  then  attached  to 
an  air  pump  and  as  much  as  possible  of  the  air  exhausted,  after  which 
the  neck  is  sealed  off  in  the  flame.  (A  better  tube  can  be  made  by  first 
sealing  off  both  ends  and  then  exhausting  through  a  side  tube.) 

By  allowing  the  shot  and  paper  to  rest  in  one  end  of  the  tube  and 
then  inverting  the  tube  quickly  they  can  be  made  to  fall  the  length  of 
the  tube  without  being  retarded  by  the  air. 


MECHANICS  27 

tation.  The  rate  at  which  bodies  acquire  potential 
energy  when  raised  above  the  earth  is  proportional  to 
their  weight,  hence  in  falling  they  must  acquire  kinetic 
energy  in  proportion  to  their  weight. 

Kinetic  Energy  of  Moving  Body  Independent  of  its 
Weight.  —  But  the  kinetic  energy  which  a  body  has  at 
a  given  time  is  not  affected  by  the  gravitation  pressure 
upon  it,  hence  is  independent  of  its  weight.  The 
kinetic  energy  of  a  body  may  enable  it  to  do  work 
while  rising  against  gravitation,  hence  in  spite  of  its 
weight.  The  heavy  fly  wheel  of  an  engine  can  acquire 
no  energy  from  gravitation,  since  one  half  of  the  wheel 
is  moving  against  the  gravitation  attraction  as  fast  as 
the  other  half  is  moving  with  it.  Such  a  wheel  when 
in  rapid  motion  has  a  large  quantity  of  kinetic  energy 
and  may  do  a  corresponding  quantity  of  work  before 
it  is  brought  to  rest. 

Definition  of  Mass.  —  The  capacity  which  a  body 
has  for  acquiring  kinetic  energy  accordingly  varies  just 
as  the  weight  of  the  body  varies,  but  it  is  not  caused 
by  the  weight  of  the  body.  It  has  been  thought  to  be 
due  to  the  quantity  of  matter  which  the  body  contains, 
and  this  quantity  has  been  called  the  Mass  of  the  body. 
The  attraction  of  gravitation,  which  is  the  cause  of  the 
weight  of  a  body,  accordingly  varies  as  the  mass  of  the 
body;  and  the  capacity  which  a  body  has  for  acquiring 
kinetic  energy  also  varies  as  its  mass.  The  potential 
energy  of  the  bodies  which  we  have  been  considering 
depends  upon  the  weight  of  the  bodies  ;  their  kinetic 
energy  is  independent  of  their  weight,  and  would  be 
the  same  if  gravitation  should  cease  to  act  upon  them. 

Indestructibility  of  Mass.  —  The  mass  of  a  body  is 
the  only  known  property  of  the  body  which  cannot  be 


Or  THE 

UNIVP-Doi-rv 


28  PHYSICS 

changed  by  chemical  action.  Bodies  of  various  kinds 
have  been  sealed  in  glass  tubes  and  allowed  to  react 
chemically  upon  each  other,  thus  changing  all  their 
other  physical  properties,  but  their  weights  and  their 
capacities  for  acquiring  kinetic  energy  were  not  appre- 
ciably changed. 

Relation  of  Weight  to  Mass. — Since  the  mass  of  a 
body  is  commonly  accepted  as  the  measure  of  the 
quantity  of  material  which  it  contains,  we  need  to  fre- 
quently determine  the  masses  of  bodies.  In  common 
practice  this  is  done  by  comparing  the  weights  of  the 
bodies  with  the  weights  of  standard  units  of  mass. 
Since  weight  varies  with  a  variation  in  the  gravitation 
attraction,  the  weight  of  the  same  body  may  be  differ- 
ent under  different  conditions.  Thus  the  gravitation 
attraction  on  the  moon  is  only  one  sixth  of  what  it  is 
on  the  earth,  and  a  body  transported  to  the  moon  would 
have  only  one  sixth  of  its  weight  when  on  the  earth. 
If  two  masses  which  are  of  the  same  weight  on  the 
earth  were  transported  to  the  moon,  they  would  still 
be  of  the  same  weight  there,  hence  in  the  comparison 
of  masses  by  means  of  their  weight  a  change  of  the 
gravitation  attraction  would  not  affect  the  result. 

INERTIA 

Definition. — The  fact  that  work  must  be  done  upon 
a  body  to  set  it  in  motion,  and  that  a  body  in  motion 
cannot  stop  without  doing  work  upon  another  body,  is 
sometimes  said  to  be  due  to  the  Inertia  of  the  body. 
A  body  which  requires  more  work  than  another  to  give 
it  the  same  velocity  is  said  to  have  more  inertia  than 
the  other,  When  used  in  this  sense,  inertia  means  the 


MECHANICS  29 

same  thing  as  mass.      There  are  no  units  of  inertia,  so 
the  inertia  of  a  body  is  never  measured. 

FALLING   BODIES 

Gravitation  and  Falling  Bodies. — Bodies  falling 
freely  toward  the  earth  soon  acquire  a  velocity  so  great 
as  to  be  difficult  of  measurement.  To  overcome  this 
difficulty  and  make  observation  more  convenient 
various  devices  are  used  for  slowing  down  their  motion. 
One  such  device  is  to  allow  the  body  in  the  form  of  a 
ball  or  cylinder  to  roll  down  an  inclined  plane.  We 
have  seen  that  it  requires  the  same  amount  of  work  to 
raise  a  body  to  a  given  height  on  any  inclined  plane, 
consequently  gravitation  will  do  the  same  amount  of 
work  on  a  body  rolling  from  the  same  vertical  height 
down  any  inclined  plane.  The  velocity  which  the 
body  will  have  at  the  foot  of  the  plane  will  accordingly 
depend  only  upon  the  height  of  the  plane,  and  not  at 
all  upon  its  length.  By  making  the  plane  very  long 
as  compared  with  its  height  the  ball  will  roll  down  it 
very  slowly,  and  the  space  passed  through  in  succes- 
sive periods  of  time  can  be  measured.  This  device  for 
studying  the  laws  of  falling  bodies  was  first  used  by 
Galileo. 

Atwood's  Machine. — Another  device  in  common 
use  in  studying  the  laws  of  falling  bodies  is  to  compel 
the  falling  body  to  raise  another  body  almost  equal  to 
itself  in  weight.  In  this  way,  most  of  its  potential 
energy  is  transferred  to  the  other  body,  and  its  gain  of 
kinetic  energy  and  consequent  velocity  is  small.  The 
best  known  instrument  for  this  purpose  is  Atwood's 
Machine.  It  consists  essentially  of  a  light  fixed  pulley 
so  mounted  as  to  turn  on  its  axis  with  very  little  fric- 


3o  PHYSICS 

tion,  and  a  vertical  scale  on  which  the  distances  fallen 
by  the  body  in  successive  intervals  of  time  can  be 
measured.  A  long  thread  with  equal  weights  attached 
to  its  ends  is  placed  over  the  pulley,  and  a  small  addi- 
tional weight  in  the  form  of  a  light  rider  is  placed  upon 
one  of  the  weights.  The  excess  of  potential  energy 
on  the  side  of  the  rider  sets  in  motion  both  weights  and 
the  pulley,  but  since  only  the  potential  energy  of  the 
rider  is  employed  in  moving  the  whole  system,  the 
motion  is  much  slower  than  in  a  freely  falling  body, 
and  by  choosing  a  light  enough  rider  the  motion  can 
be  made  as  slow  as  desired. 

Experiments  with  Atwood's  Machine.* 

LABORATORY  EXERCISE  17. — Place  a  light  rider  of  known 
weight  on  the  suspended  weight  of  the  Atwood's  Machine 
which  hangs  in  front  of  the  scale.  Taking  hold  of  the  cord 
on  the  other  side  of  the  pulley,  draw  it  down  until  the 
bottom  of  the  rider  is  exactly  even  with  the  zero  at  the  top 
of  the  scale.  Start  the  metronome  or  seconds  pendulum, 
and  release  the  cord  exactly  upon  one  of  the  ticks.  Move 
the  ring  which  serves  to  catch  the  rider  into  such  a  position 
that  it  will  stop  the  rider  exactly  upon  the  next  tick  after  the 
cord  is  released.  To  do  this,  adjust  the  height  of  the  ring 
so  that  the  tick  of  the  pendulum  and  the  click  of  the  rider 
upon  the  ring  will  be  heard  exactly  together.  (The  weight 
and  rider  should  not  fall  more  than  eight  or  ten  centimeters 
in  the  first  second.) 

To  find  the  space  passed  through  by  the  weight  in  the  first 
second  after  the  rider  is  removed,  adjust  the  movable  shelf 
so  that  the  click  of  the  weight  upon  it  will  be  heard  exactly 
with  the  second  tick  of  the  pendulum.  Notice  that  the  dis- 
tance from  the  ring  to  the  shelf  must  be  decreased  by  the 
height  of  the  weight  to  give  the  distance  fallen  in  one  second. 

Adjust  the  shelf  so  that  it  will  stop  the  weight  at  the  end 
of  the  second,  third,  arid  following  seconds  of  its  fall.  Does 

*  If  desired  by  the  teacher,  these  experiments  may  be  performed  on 
the  inclined  plane.  The  necessary  modifications  are  easily  made. 


MECHANICS 


31 


the   weight    fall    with    uniform    velocity    after   the   rider   is 
removed  ? 

How  does  the  velocity  acquired  by  the  weight  and  rider 
in  one  second  compare  with  their  mean  velocity  during  that 
second  ? 

If  the  weight  and  rider  had  fallen  20  centimeters  in  one 
second,  how  far  would  the  weight  have  fallen  in  one  second 
after  the  rider  was  removed  ? 

Repeat  your  experiments,  leaving  the  rider  on  the  weight 
for  two  seconds  of  its  fall.  How  does  the  velocity  which 
the  weight  and  rider  acquire  in  two  seconds  compare  with 
the  velocity  which  they  acquire  in  one  second  ? 

Find  the  velocity  acquired  by  the  weight  and  rider  in 
•three  seconds. 

Letting  /  =  time  of  fall  with  rider, 
v  =  velocity  acquired,  and  £  —  space 
passed  through  by  weight  and  rider  in 
time  /,  tabulate  your  results  in  the  fol- 
lowing form.  Complete  the  table  for 
as  many  seconds  as  the  height  of  the 
machine  will  permit. 

Repeat  the  preceding  experiments 
with  another  rider  twice  as  heavy  as 
the  first. 

In  your  experiments  with  Atwood's  Machine  you 
have  found  the  weight  and  rider  to  fall  with  an  increas- 
ing velocity.  When  the  velocity  of  a  moving  body  is 
increasing  or  decreasing,  the  body  is  said  to  have 
accelerated  motion. 

ACCELERATION 

Definition  of  Acceleration. — The  rate  of  change  of 
velocity  of  a  body,  or,  what  is  the  same  thing,  the 
change  of  velocity  in  the  unit  of  time,  is  called 
Acceleration. 

Uniform  Acceleration. — When  the  change  of  velocity 
in  each  unit  of  time  is  the  same,  the  acceleration  is  said 
to  be  uniform. 


32  PHYSICS 

Positive  and  Negative  Acceleration. — When  the 
velocity  is  increasing,  the  acceleration  is  said  to  be 
positive ;  when  the  velocity  is  decreasing,  the  accelera- 
tion is  called  negative. 

Acceleration  of  Falling  Bodies. — Referring  to  the 
tabulated  results  of  your  experiments,  answer  the  fol- 
lowing questions: 

(1)  What  was  the  acceleration  of  the  weights  and  rider 
first  used  during  the  first  second  of  fall  ? 

(2)  Was  the  acceleration  uniform   as   long  as  the    rider 
remained  on  the  weight  ? 

(3)  Did  the  weights  have  an  acceleration  after  the  rider' 
was  removed  ? 

(4)  Did  the  accelerations  produced  by  the  two  riders  bear 
any  relation  to  the  weights  of  the  riders  ? 

(5)  How  did  the  velocity  acquired  by  the  weights    and 
rider  vary  with  the  time  of  fall  ? 

(6)  Using  /,  v,  and  £  with  the  same  significance  as  before, 
and  letting  a  represent  the  acceleration  of  the  weights  and 
rider  in  the  first  second,  give  an  expression  for  v  in  terms  of 
a  and  /. 

(7)  Give  an  expression  for  S  in  terms  of  a  and  /.     In 
terms  of  a  and  v. 

Magnitude  of  the  Gravitation  Acceleration. — We 
have  seen  that  the  effect  of  gravitation  upon  an  unsup- 
ported body  is  to  give  it  a  uniform  acceleration  toward 
the  earth.  The  amount  of  this  acceleration  on  a  freely 
falling  body  cannot  be  accurately  determined  by  the 
Atwood's  Machine,  since  the  falling  body  is  constantly 
giving  off  energy  to  other  parts  of  the  machine.  Care- 
ful experiments  have  shown  that  in  the  latitude  of  the 
United  States  the  acceleration  of  gravity  on  a  freely 
falling  body  not  sensibly  retarded  by  the  air  is  about 
32.16  feet  or  980  centimeters  a  second. 

Since  the  space  passed  through  by  a  falling  body  in 
one  second  is  numerically  equal  to  half  the  acceleration 


MECHANICS  33 

acquired  in  the  same  time,  a  body  not  retarded  by  the 
air  will  fall  16.08  feet  or  490  centimeters  in  one  second. 

PROBLEMS. — The  symbol  generally  used  for  the  acceleration 
of  gravity  is  g.  Substituting  the  above  numerical  value  of 
g  for  a  in  your  Atwood's  Machine  equations,  what  velocity 
will  a  freely  falling  body  acquire  in  five  seconds  ?  How  far 
will  it  fall  in  five  seconds  ?  How  far  in  the  fifth  second  ? 

Since  a  body  projected  vertically  upward  loses  velocity  as 
fast  as  a  falling  body  acquires  it,  with  what  velocity  must  a 
body  be  projected  upward  in  order  to  rise  for  two  seconds  ? 

Since  a  falling  body  loses  potential  energy  and  gains 
kinetic  energy  at  the  same  rate,  its  gain  of  kinetic  energy 
must  be  proportional  to  the  space  through  which  it  falls. 
Thus  a  pound  mass  in  falling  ten  feet  must  acquire  ten  foot- 
pounds of  kinetic  energy.  Calling  the  value  of  g  32  feet, 
how  much  kinetic  energy  will  a  pound  mass  gain  in  falling 
for  one  second  ?  For  two  seconds  ?  For  three  seconds  ? 

How  does  the  kinetic  energy  of  a  falling  body  vary  with 
the  time  of  fall  ? 

A  body  projected  upward  with  velocity  V  rises  to  height 
H;  with  what  velocity  must  it  be  projected  upward  to  rise 
to  height  4^T? 

A  body  with  velocity  V  has  kinetic  energy  E\  what  is  its 
kinetic  energy  when  its  velocity  is  2  F?  When  its  velocity 
is3F? 

A  body  having  a  mass  of  four  pounds  has  a  velocity  of  96 
feet  a  second;  how  many  foot-pounds  of  kinetic  energy  has 
it  ?  (To  what  height  could  this  velocity  carry  it  ?) 

UNIVERSALITY   OF   GRAVITATION 
Gravitation  Acceleration  of  the  Moon.  —  It  was 

shown  by  Newton  that  the  motion  of  the  moon  around 
the  earth  indicates  that  the  moon  has  an  acceleration 
toward  the  earth  of  about .  i  inch  per  second.*  In  order 
for  this  acceleration  to  be  due  to  gravitation,  the  accel- 
eration of  gravitation  for  bodies  above  the  earth's 
surface  must  decrease  as  the  squares  of  their  distances 

*  For  demonstration,  see  foot-note,  page  37;  also  page  55. 


34  PHYSICS 

from  the  center  of  the  earth  increase.  Thus  the  moon 
is  sixty  times  as  far  from  the  center  of  the  earth  as  a 
body  on  the  earth's  surface,  while  its  acceleration 
toward  the  earth  is  ¥^7¥  as  great  as  that  of  bodies  on 
the  surface  of  the  earth. 

Gravitation  Accelerations  of  the  Planets  and 
Satellites. — Newton  also  found  that  the  movements  of 
the  satellites  of  Jupiter  about  their  planet  showed 
accelerations  toward  Jupiter  decreasing  as  the  squares 
of  their  distances  from  the  planet  increase,  hence  he 
concluded  that  gravitation  acts  upon  Jupiter  as  upon 
the  earth.  But  the  earth  and  other  planets  of  the 
Solar  System  have  accelerations  toward  the  sun  vary- 
ing inversely  as  the  squares  of  their  distances  from  the 
sun,  so  gravitation  apparently  acts  throughout  the 
Solar  System.  There  are  also  many  very  distant 
double  stars  which  revolve  around  each  other,  hence 
which  have  accelerations  toward  each  other.  The 
distances  between  these  stars  cannot  be  measured,  but 
since  they  are  known  to  be  made  of  the  same  sub- 
stances as  are  the  bodies  of  the  Solar  System,*  their 
accelerations  are  probably  due  to  gravitation. 

Since  Newton  was  the  first  to  discover  the  apparent 
universality  of  gravitation,  his  statement  of  the  theory 
has  come  to  be  known  as  Newton's  Law  of  Gravitation. 

Newton's  Law  of  Gravitation. — Every  particle  of 
matter  in  the  universe  is  attracted  directly  toward  every 
other  particle  with  a  force  varying  directly  as  the  mass 
of  each  particle,  and  inversely  as  the  square  of  the  dis- 
tance between  them. 

From  what  experiment  have  we  previously  concluded  that 
gravitation  varies  as  the  mass  ? 

*  See  paragraph  on  Absorption  Spectra  of  the  Stars. 


MECHANICS  35 


FORCE 

Definition  of  Force. — The  physicists  of  the  time  of 
Newton  had  no  notion  of  energy  as  one  of  the  constants 
of  the  physical  universe,  and,  following  the  mechanics 
of  Galileo,  they  assumed  that  when  an  acceleration 
takes  place  in  some  part  of  a  material  system  *  it  is  due 
to  a  ' '  force  ' '  exerted  by  some  other  part  of  the  system. 
Newton  accordingly  speaks  of  gravitation  as  a  force, 
and  he  regarded  the  weight  of  a  body  as  a  measure  of 
the  attractive  force  exerted  upon  it  by  the  earth. 
Newton  defined  force  as  follows:  "  Impressed  force  is 
action  exercised  on  a  body  so  as  to  change  its  state  of 
rest  or  of  uniform  motion  in  a  straight  line. ' '  This 
assumes  that  a  body  at  rest  will  remain  at  rest  or  a 
body  in  motion  will  continue  to  move  uniformly  in  a 
straight  line  unless  acted  upon  by  a  force.  Expressed 
in  the  language  which  we  have  been  using,  A  force  is 
whatever  produces  an  acceleration. 

Measurement  of  Force. — Newton  states  that  in  his 
day  the  term  force  was  measured  in  various  ways,  that 
is,  that  there  was  no  general  agreement  as  to  how  a 
force  should  be  measured.  He  accordingly  suggested 
a  definition  for  the  measure  of  a  force  which  has  been 
generally  used  since  his  time.  His  definition  of  force 
and  his  notion  as  to  what  should  be  regarded  as  the 
measure  of  a  force  are  contained  in  his  three  laws  of 
motion. 

*  By  a  material  system  is  meant  that  part  of  the  material  universe 
which  is,  for  the  time  being,  the  subject  of  investigation.  It  may  be  a 
single  material  particle,  a  body  or  number  of  bodies,  or  it  may  include 
the  whole  material  universe. 


36  PHYSICS 

Newton's  Laws  of  Motion. 

LA  W  I.  Every  body  perseveres  in  its  state  of  rest  cr 
of  uniform  motion  in  a  straight  line  unless  it  is  com- 
pelled to  change  that  state  by  impressed  forces. 

LA  W  II.  Change  of  motion  is  proportional  to  the 
impressed  force  and  takes  place  in  the  direction  in 
which  the  force  is  impressed. 

LA  W  III.  To  every  action  there  is  always  an  oppo- 
site and  equal  reaction,  or  the  mutual  actions  of  two 
bodies  are  always  equal  and  opposite. 

It  will  be  seen  that  the  first  law  merely  includes  the 
definition  of  a  force,  i.e.,  "  action  exercised  on  a  body 
so  as  to  change  its  state  of  rest  or  of  uniform  motion 
in  a  straight  line. ' '  Stated  in  the  language  of  energy 
the  first  law  would  be :  Every  body  perseveres  in  its 
state  of  rest  or  of  uniform  motion  in  a  straight  line 
unless  it  receives  energy  from  or  gives  off  energy  to 
some  other  body.  That  is,  every  change  in  the 
velocity  of  a  body  is  due  to  a  change  in  its  kinetic 
energy.  A  body  moving  with  a  uniform  velocity  in  a 
straight  line  is  neither  gaining  nor  losing  kinetic 
energy.* 

*  If  it  be  true  that  a  moving  body  not  acted  upon  by  a  force  will  pro- 
ceed in  a  straight  line,  then  every  example  of  motion  in  a  curved  line 
indicates  the  existence  of  a  force.  When  this  force  ceases  to  act,  the 
body  will,  according  to  the  first  law,  proceed  in  a  straight  line  in  the 
direction  in  which  it  happened  to  be  moving  at  the  instant  when  the 
force  disappeared.  Thus  the  particles  of  mud  thrown  from  a  revolving 
wheel  start  off  in  straight  lines  tangent  to  the  circumference  of  the 
wheel,  instead  of  continuing  to  circle  round  the  wheel.  A  stone  thrown 
from  a  sling  is  another  good  illustration  of  the  first  law.  The  stone  is 
held  in  the  sling  and  is  swung  around  the  hand  until  it  acquires  a  high 
velocity  and  is  released  at  the  instant  when  it  is  going  in  the  desired 
direction.  While  the  stone  remained  in  the  sling  it  was  constrained 
by  a  force  which  prevented  it  from  getting  farther  from  the  hand.  To 


MECHANICS 


37 


In  the  second  law,  Newton  defines  his  proposed 
measure  of  force.  He  says  that  the  magnitude  of  the 
impressed  force  shall  be  regarded  as  proportional  to  the 
change  of  motion  which  it  produces.  Before  we  can 
measure  the  magnitude  of  a  force  we  must  accordingly 
have  some  way  of  measuring  the  quantity  of  motion  of 
a  given  body,  otherwise  we  cannot  tell  what  change 
has  been  produced  in  this  quantity  of  motion.  Newton 
had  previously  defined  quantity  of  motion  as  the 
product  of  the  mass  of  the  moving  body  into  its  velocity. 
That  is,  quantity  of  motion  =  mv. 

Momentum. — The  quantity  represented  by  mv  we 
now  call  Momentum.  Hence  the  magnitude  of  a  force 
is  measured  by  the  change  of  momentum  which  it  will 
produce  in  a  unit  of  time. 

Since  a  force  does  not  change  the  mass  of  a  body,  it 
can  change  its  momentum  only  by  changing  its  velocity, 


compel  a  body  to  move  in  a  circle,  it  must  accordingly  be  acted  upon  by 

a  force  impelling  it  toward  the  center  of  the 

circle. 

Thus  let  a  be  a  particle  moving  in  a  circle 
about  the  center  c  with  a  velocity  which 
will  carry  it  to  b  in  one  second.  At  the  instant 
when  the  particle  is  at  a  it  is  moving  at  right 
angles  to  the  radius  ac,  that  is,  in  the  di- 
rection ad.  If  it  has  at  the  same  time  an 
acceleration  toward  c  which  will  carry  it 
to  e  in  the  time  that  its  velocity  in  a  straight 
line  will  carry  it  to  d,  it  will  reach  b  in  the 
same  time  that  it  would  otherwise  have  re- 
quired to  reach  d. 

In  the  same  manner,  it  will  at  the  end  of  the  next  second  reach  b'  in- 
stead of  d'.  Consequently  a  particle  moving  in  the  circle  abb'  with  a 
velocity  ab  must  have  besides  its  uniform  rectilinear  velocity  ad  an 
acceleration  toward  the  center  of  the  circle  which  will  carry  it  through 
the  space  ae  in  one  second. 


FIG.  ii. 


38  PHYSICS 

that  is,  by  giving  it  an  acceleration ;  hence  a  force  is 
whatever  produces  acceleration. 

The  Force  Equation. — Since  change  of  momentum 
is  proportional  to  change  of  velocity,  that  is,  propor- 
tional to  acceleration,  a  force  which  is  measured  by  the 
change  of  momentum  in  a  unit  of  time  is  measured 
by  the  mass  times  the  acceleration  which  is  given  it 
by  the  force.  The  formula  for  force  is  accordingly 
F  =  ma . 

Definition  of  Constant  Force. — A  constant  force  is 
one  which  produces  the  same  change  of  momentum  in 
each  unit  of  time,  that  is,  one  which  gives  uniform 
acceleration.  Is  the  weight  of  a  body  near  the  surface 
of  the  earth  a  constant  force  ? 


FORCE   UNITS 

The  Poundal, — The  unit  of  force  in  the  English 
system  of  weights  and  measures  is  the  poundal.  It  is 
defined  as  the  force  which  would  give  to  a  mass  of  one 
pound  an  acceleration  of  one  foot  per  second. 

Since  the  gravitation  acceleration  is  32  feet  per 
second,  the  force  of  gravitation  on  a  pound  mass  is  32 
poundals. 

The  Dyne. — The  unit  of  force  in  the  metric  system 
is  the  Dyne.  It  is  defined  as  the  force  which  would 
give  to  a  mass  of  one  gram  an  acceleration  of  one 
centimeter  per  second. 

Since  the  acceleration  of  gravitation  is  980  centi- 
meters a  second,  the  weight  of  a  gram  in  force  units  is 
980  dynes. 

The  product  of  a  mass  in  pounds  into  an  acceleration 
in  feet  per  second  gives  a  force  in  poundals. 


MECHANICS  39 

The  product  of  a  mass  in  grams  into  an  acceleration 
in  centimeters  per  second  gives  a  force  in  dynes. 

PROBLEMS. — Upon  what  mass  is  the  force  of  gravitation 
equal  to  one  poundal  ? 

A  force  of  one  poundal  acts  for  one  second  upon  a  mass 
of  one  ounce  avoirdupois;  what  velocity  does  it  give  to  it  ? 

How  far  will  a  gram  mass  fall  in  one  second  under  an 
attraction  of  one  dyne  ? 

ACTION   AND   REACTION 

Definition  of  Action  and  Reaction. — In  his  third 
law  Newton  says  that  the  mutual  actions  of  two  bodies 
are  always  equal  and  opposite.  In  order  to  understand 
his  meaning  in  this  statement,  we  must  know  what  he 
means  by  "  action. "  This  we  may  make  out  from  his 
use  of  the  term  in  other  places.  In  defining  force  he 
says,  "  Force  is  action  exercised  on  a  body,"  etc. 
But  we  have  seen  that  force  as  a  quantity  is  measured 
by  the  change  in  momentum  which  it  produces  in  a 
unit  of  time,  hence  the  '  *  action  ' '  spoken  of  in  the  third 
law  must  be  measured  by  the  change  of  momentum 
which  it  produces.  Used  in  this  sense,  the  third  law 
states  that  when  two  bodies  act  upon  each  other  so  that 
one  body  gains  momentum  in  a  given  direction,  the 
other  loses  an  equal  quantity  of  momentum  in  the  same 
direction  or  gains  the  same  quantity  of  momentum  in 
the  opposite  direction. 

The  fact  that  there  is  often  such  a  mutual  gain  of 
momentum  in  opposite  directions  is  so  well  known  as 
to  need  no  experimental  proof.  The  recoil  of  a  gun 
when  it  is  fired,  the  rotary  motion  of  the  common  lawn- 
sprinkler,  the  backward  motion  given  to  a  boat  when 
one  jumps  from  it,  are  good  examples. 


40  PHYSICS 

Equality  of  Action  and  Reaction. — The  equality  of 
momentum  in  action  and  reaction  can  be  proved 
experimentally  in  many  cases,  while  in  others  it  can 
only  be  inferred.  This  equality  in  the  case  of  a  falling 
body  assumes  that  the  earth  acquires  as  much  momen- 
tum toward  the  body  as  the  body  acquires  toward  the 
earth.  On  account  of  the  great  mass  of  the  earth,  its 
acceleration  toward  a  falling  body  is  ordinarily  in- 
appreciable, but  in  the  case  of  the  moon's  attraction  it 
appears  in  the  form  of  the  tidal  waves. 

In  the  case  of  a  man  sitting  in  a  boat  and  holding 
one  end  of  a  rope  while  another  man  walks  on  the 
shore  and  tows  the  boat  by  the  rope,  we  see  at  first  an 
apparent  exception  to  the  law.  It  is  easy  to  see  that 
both  men  must  pull  equally  upon  the  rope,  that  is,  if 
between  each  man's  hand  and  the  rope  there  was  a 
spring  balance  these  balances  would  indicate  equal 
pulls ;  but  if  we  consider  only  the  men  and  the  boat, 
the  momentum  seems  to  be  all  in  one  direction. 
When  we  consider  the  fact  that  the  man  who  has  been 
walking  has  pushed  backward  upon  the  earth  as  much 
as  he  has  pulled  forward  upon  the  boat,  we  can  see 
that  when  we  take  into  consideration  all  the  bodies 
concerned  the  momentums  in  opposite  directions  may 
still  be  equal.  This  would  be  seen  at  once  if  the  man 
who  tows  the  boat  were  walking  along  the  deck  of  a 
larger  boat  while  pulling.  The  two  boats  would  then 
move  toward  each  other  with  velocities  (neglecting  the 
friction  of  the  water)  inversely  proportional  to  their 
masses. 

Restatement  of  Newton's  Third  Law.— The  third 
law  of  motion  may  accordingly  be  stated  as  follows: 
No  mutual  action  between  the  parts  of  a  material 


MECHANICS  41 

system  can  change  the  momentum  of  the  system  as  a 
whole;  or,  No  mutual  action  between  the  parts  of  a 
material  system  can  give  motion  to  the  center  of  gravity 
of  the  system.  This  is  equivalent  to  applying  the  first 
law  to  systems  made  up  of  several  bodies.  Thus, 
Every  system  of  material  bodies  perseveres  in  its  state 
of  rest  or  of  uniform  motion  in  a  straight  line  unless  it 
is  compelled  to  change  that  state  by  forces  impressed 
from  without  the  system. 

Direction  of  Momentum. — In  his  second  law  Newton 
says:  "Change  of  motion  is  proportional  to  the  im- 
pressed force  and  takes  place  in  the  direction  in  which  the 
force  is  impressed. ' '  Hence  in  describing  a  momentum 
it  is  always  necessary  to  give  its  direction.  When  mo- 
mentum in  a  given  direction  is  called  positive,  mo- 
mentum in  the  opposite  direction  must  be  called  nega- 
tive, otherwise  the  third  law  of  motion  will  not  apply. 

Momentum  of  Rebounding  Ball. — Thus  a  ball  is 
thrown  perpendicularly  against  a  wall  and  rebounds 
with  the  same  velocity  with  which  it  struck  the  wall. 
Its  momentum  before  striking  was  mv  toward  the  wall ; 
its  momentum  after  the  rebound  is  mv  in  the  opposite 
direction,  or  —  mv.  In  order  that  the  third  law  of 
motion  may  apply,  we  must  assume  that  it  has  given 
to  the  wall  the  momentum  +  mv,  and  has  taken  from 
the  wall  the  momentum  —  mv,  which  is  equivalent  to 
giving  to  the  wall  altogether  a  momentum  .+  2mv. 

Persistence  of  Momentum  in  Elastic  Impact. 

LABORATORY  EXERCISE  18. — Two  "collision  balls"*  of 
equal  mass  are  suspended  so  as  to  form  pendulums  of  the 
same  length  and  so  that  when  at  rest  their  surfaces  just  touch 
each  other.  They  are  best  made  by  suspending  each  ball 

*  The  best  collision  balls  are  usually  made  of  ivory.  Steel  balls  are 
quite  as  good,  and  may  usually  be  more  easily  obtained. 


42  PHYSICS 

from  two  threads  or  fine  wires  separated  at  the  top,  so  that 
the  balls  can  swing  in  only  one  plane,  and  this  should  be 
the  vertical  plane  in  which  both  balls  rest  when  in  equilib- 
rium. A  scale  placed  to  one  side  of  the  balls  is  convenient. 

Draw  one  ball  a  measured  distance  to  one  side  and  let  it 
swing  against  the  other  ball.  Does  the  second  ball  gain  as 
much  momentum  as  the  first  ball  loses  ? 

Separate  the  balls  by  pulling  both  aside  to  equal  distances 
and  allow  them  to  swing  together.  Calling  momentum  in 
one  direction  -j-  and  in  the  other  direction  — ,  the  algebraic 
sum  of  the  momentums  at  the  instant  of  impact  is  zero; 
does  it  remain  zero  ? 

Replace  one  of  the  balls  by  a  smaller  one,  making  the  two 
pendulums  of  the  same  length  and  suspending  them  so  that 
they  will  touch  as  before.  They  will  now  swing  in  the  same 
time,  and  as  the  time  of  vibration  of  each  is  nearly  inde- 
pendent of  its  arc,  the  velocities  with  which  they  reach  the 
centers  of  their  arcs  will  be  proportional  to  the  distances 
through  which  they  swing.  If  their  masses  are  known,  their 
relative  momentums  can  be  calculated  by  multiplying  their 
masses  by  the  distances  through  which  they  swing  before 
reaching  the  centers  of  their  arcs. 

Pull  the  heavy  ball  to  one  side  and  let  it  swing  against 
the  lighter  one,  and  determine  if  it  loses  as  much  momentum 
as  the  lighter  one  gains. 

Let  the  lighter  ball  swing  against  the  heavy  one>  Before 
striking,  it  had  a  certain  positive  momentum.  After  strik- 
ing, it  rebounds,  and  accordingly  has  negative  momentum. 
Is  the  momentum  acquired  by  the  larger  ball  the  algebraic 
sum  of  the  momentum  received  from  and  the  momentum 
given  off  to  the  smaller  ball  ? 

Does  the  smaller  ball  give  to  the  larger  one  more  momen- 
tum than  it  itself  had  before  impact  ? 

FORCE   AND   WORK 

Force  One  Factor  in  Work. — We  have  seen  that  a 
force  is  measured  by  the  formula  F  =  ma,  and  that  a 
force  in  poundals  is  measured  by  the  mass  in  pounds 
times  the  acceleration  in  feet  per  second.  Our  unit  of 


MECHANICS  43 

work  in  the  corresponding  system  is  the  foot-pound, 
and  we  have  seen  that  it  is  the  work  done  in  raising  a 
pound  mass  one  foot  against  gravitation.  But  the  force 
of  gravitation  on  a  pound  is  32  poundals,  hence  to 
overcome  a  force  of  32  poundals  through  one  foot 
requires  the  expenditure  of  one  foot-pound  of  energy. 

In  considering  the  relation  of  force  and  work  there 
are  accordingly  two  factors  to  be  considered,  the  force, 
and  the  distance  through  which  it  is  said  to  act  or 
through  which  it  resists  action. 

Equation  for  Force  and  Work. — Letting  W  stand 
for  work,  we  have  seen  that  F  (in  poundals)  X  S 

W 
(in  feet)  =  -  —  (in  foot-pounds),  or  $2FS  =  W. 

The  Erg. — The  unit  of  work  in  the  C.G.S.*  system 
is  the  Erg.  It  is  the  work  done  in  moving  a  body  one 
centimeter  against  a  force  of  one  dyne. 

Since  the  weight  of  a  gram  is  980  dynes,  980  ergs 
of  work  must  be  done  in  raising  one  gram  through  a 
height  of  one  centimeter.  Almost  one  erg  of  work  is 
done  in  raising  a  milligram  through  one  centimeter. 

Since  a  mass  of  one  gram  will  acquire  a  velocity  of 
one  centimeter  a  second  from  a  force  of  one  dyne,  it 
will  move  only  -J  centimeter  in  that  time,  consequently 
a  dyne  acting  for  a  second  on  a  gram  will  do  £  erg 
of  work. 

*  Since  the  system  of  units  based  upon  the  centimeter,  gram,  and  sec- 
ond (called  the  C.G.S.  system)  is  used  in  most  scientific  works,  the 
student  should,  as  soon  as  possible,  become  familiar  with  the  metric 
system  of  weights  and  measures..  This  can  best  be  done  by  weighing 
and  measuring  bodies  with  metric  units.  Comparisons  should  be  made 
with  the  corresponding  units  in  the  two  systems.  This  is  necessary 
work,  but  it  is  not  Physics,  and  should  be  done  when  needed  as  a 
preparation  for  the  work  of  Physics. 


44 


PHYSICS 


ft 


PROBLEMS  ON  FORCE  AND  WORK. — What  acceleration  will 
a  dyne  give  to  two  grams  in  one  second  ?  How  far  will  the 
two  grams  move  in  the  second  ?  How  much  work  will  a 
dyne  do  upon  two  grams  in  a  second  ? 

How  far  will  a  gram  move  in  two  seconds  under  the  force 
of  a  dyne  ?  How  much  energy  will  it  acquire  ? 

Tabulate  velocity  and  kinetic  energy  of  a  gram  under  the 
force  of  a  dyne  for  four  seconds,  as  follows: 

Show  that  when  the  mass  is  meas- 
ured in  grams  and  the  velocity  in 
centimeters  a  second,  the  kinetic  energy 
in  ergs  can  be  calculated  from  the 

mv* 
equation  JL  =  — . 

The  acceleration  of   gravity  is  980 
centimeters   a    second,    what    kinetic 
energy  would  a  gram  acquire  in  falling 
freely  for  one  second  ? 
A  mass  of  5  grams  has  an  acceleration  of  20  centimeters 
a  second.      What  force  is  acting  upon  it  ?     What   kinetic 
energy  will  it  acquire  in  4  seconds  ? 

A  mass  of  5  grams  is  acted  upon  by  a  force  of  20  dynes; 
what  kinetic  energy  will  it  acquire  in  4  seconds  ? 

Show  that  where  the  mass  is  measured  in  pounds  and  the 
velocity  in  feet  per  second,  the  kinetic  energy  in  foot-pounds 

mv* 
is  given  by  the  equation  E  —  — . 

What  kinetic  energy  will  a  five-pound  mass  acquire  in 
falling  freely  for  four  seconds  ? 

Why   must   the  equation  E  =  —  which  applies   to   the 

units  of  the  C.G.S.  system  be  divided  by^  to  give  the  kinetic 
energy  in  the  foot-pound  system  ? 

Show  that  the  potential  energy  of  a  body  raised  above  the 
earth  is  expressed  in  the  C.G.S.  system  by  mght  where  h  is 
the  height  in  centimeters  to  which  the  body  is  raised. 

Give  the  corresponding  expression  for  the  potential  energy 
of  a  body  in  foot-pounds. 

Potential. — It  is  customary,  especially  in  the  calcu- 
lation of  electrical  energy,  to  speak  of  the  ' '  Potential  ' ' 


MECHANICS  45 

of  a  point  in  space,  meaning  the  potential  energy  which 
a  unit  quantity  of  electrification  or  a  unit  mass  in  grams 
would  have  if  located  at  that  point.  The  Gravitation- 
potential  in  ergs  of  a  point  above  the  earth  is  the 
number  which  tells  how  many  ergs  of  potential  energy 
a  gram  mass  would  have  if  raised  to  that  point. 

The  symbol  V  is  generally  used  to  indicate  a  poten- 
tial. In  the  case  of  the  gravitation-potential,  V  =  ghy 
where  V  is  expressed  in  ergs.  The  potential  energy 
of  a  body  raised  above  the  earth  is  accordingly  E  = 
m  V  =  mgh. 

The  potential  in  foot-pounds  of  a  point  above  the 
earth  is  V  =  h,  where  h  is  expressed  in  feet. 

What  is  the  potential  in  ergs  of  a  point  5  meters  above 
the  earth  ? 

GENERAL  EQUATIONS  OF  MECHANICS 

The  relations  which  we  have  been  considering 
between  velocity,  acceleration,  force,  momentum,  and 
work,  and  the  units  of  mass,  time,  and  space  as 
expressed  in  the  C.G.S.  system  may  be  shown  in  the 
following  equations: 

»••'•.»  M        W 

Force  =  F  =  ma  =  —  =  —~- ; 

Ft 

Velocity          =  v  =  at  =  — ;  / 

m 

v        F 

Acceleration  =  a  =  —  =  — ; 

t         m  ' 

Distance        —  S  =  — :  = ; 

2  2     ' 

Momentum   =  M=  mv  =  Ft\ 


46 


PHYSICS 


In  general,  when  three  of  these  quantities  are  known 
all  the  others  may  be  calculated  from  them. 

PROBLEMS. — Using  the  units  of  the  C.G.S.  system,  fill  in 
the  blanks  in  the  following  table: 


•m 

/ 

S 

V 

a 

F 

M 

W=  E 

10 

20 

IOOO 

IO 

5 

25 

4 

40 

IOO 

10 

5 

8 

10 

5 

60 

IOOO 

20 

IOO 

.01 

20 

IOO 

IOO 

2000 

20000 

180 

10 

QOOO 

20 

5 

IOO 

12 

IO 

I2OO 

COMPOSITION   AND    RESOLUTION   OF   MOTIONS 
AND    FORCES 

Composition  of  Motions. 

LABORATORY  EXERCISE  19. — We  have  seen  that  a  body 
projected  upward  has  a  negative  acceleration  equal  to  the 
positive  acceleration  which  it  would  have  if  allowed  to  fall 
freely  toward  the  earth,  hence  we  conclude  that  gravitation 
must  act  upon  a  moving  body  with  the  same  force  as  upon 
a  body  at  rest.  A  body  projected  horizontally  should, 
accordingly,  fall  to  the  earth  in  the  same  time  as  one  starting 
from  a  state  of  rest  at  the  same  height.  To  test  this  assump- 
tion, perform  the  following  experiment. 

Two  coins  are  laid  upon  a  table,  one  just  balanced  on  the 
edge,  as  at  A,  and  the  other  at  a  distance  of  a  foot  or  more 


MECHANICS 


47 


from  the  edge,  as  at  B.  A  ruler  or  meter  stick  is  placed 
upon  the  table  in  the  position  CD,  and  is  swung  rapidly 
around  Cas  a  pivot,  keeping  it  in  contact  with  coin  B  until 
it  reaches  the  edge  of  the  table.  In  this  way,  B  will  be 
projected  from  the  table  with  a  considerable  horizontal 


FIG.  12. 

velocity,  while  A  will  fall  directly  to  the  floor.     Do  they 
both  reach  the  floor  at  the  same  time  ? 

Resultant  Motion. — The  motion  of  the  coin  which 
was  projected  farthest  from  the  table  may  be  said  to 
be  a  "resultant"  of  two  motions,  the  one  the  hori- 
zontal motion  in  a  straight  line  given  to  the  coin  by 
the  ruler,  and  the  other  the  downward  accelerated 
motion  due  to  gravitation.  If  gravitation  had  not  acted 
upon  the  coin,  then,  according  to  the  first  law  of  motion, 
it  would  have  continued  to  move  uniformly  in  a  straight 
line.  If  it  had  received  no  horizontal  impulse  at  the 
start,  it  would  have  fallen  with  an  accelerated  motion 
directly  to  the  floor.  The  path  which  it  does  take  is 
neither  the  one  nor  the  other  of  the  two  mentioned, 
but  is  a  curved  line  resulting  from  the  two.  That  is, 
it  moves  with  the  same  uniform  horizontal  velocity  as 
it  would  if  not  acted  upon  by  gravitation,  and  it  falls 
to  the  floor  in  the  same  time  as  it  would  if  it  had  no 
horizontal  velocity. 


PHYSICS 


Graphical  Composition  of  Motions.  —  To  trace 
graphically  the  path  of  a  freely  falling  body  having  a 
horizontal  velocity  we  may  proceed  as  follows :  Sup- 
pose a  body  to  be  thrown  horizontally  from  the  top  of 
a  tower  144  feet  high  with  a  velocity  oi  16  feet  a 


c 


a 


•B 


U 


FIG.  13. 

second.  From  the  laws  of  falling  bodies  and  the  value 
of  g  we  know,  that  it  will  reach  the  earth  at  the  end  of 
three  seconds,  and  from  the  first  law  of  motion  we 
know  that  in  three  seconds  it  will  have  travelled  a  hori- 


MECHANICS  49 

zontal  distance  of  48  feet.  We  may  then  know,  with- 
out knowing  the  path  of  the  body,  the  place  where  it 
will  strike  the  earth.  To  project  the  path  of  the  body 
we  rule  a  sheet  of  paper  in  convenient  squares  by 
means  of  vertical  and  horizontal  lines,  and  let  the  side 
of  one  of  these  squares  represent  16  feet  (see  Fig.  13). 
Then  we  suppose  the  body  to  be  thrown  from  A  toward 
B  while  it  falls  from  A  toward  C.  During  the  first 
second  it  will  travel  1 6  feet  in  each  direction,  and  at 
the  end  of  the  second  it  will  be  at  a.  During  the  next 
second  it  will  move  the  same  distance  in  a  horizontal 
direction,  but  will  fall  through  three  times  the  vertical 
distance  fallen  in  the  first  second.  It  will  accordingly 
reach  b  at  the  end  of  the  second. 

Locate  its  position  at  the  end  of  the  third  second.  Draw 
a  line  from  A  to  the  final  position,  indicating  the  path  fol- 
lowed by  the  body  for  three  seconds. 

Indicate  in  the  same  manner  the  path  of  a  body  thrown 
horizontally  from  A  with  a  velocity  of  24  feet  a  second. 

We  have  seen  that  the  resultant  of  a  uniform  velocity  and 
an  acceleration  at  right  angles  to  each  other  is  an  accelerated 
motion  in  a  curved  path.  By  the  same  method  of  squares 
find  the  resultant  of  two  uniform  velocities  at  right  angles 
to  each  other.  Show  that  this  resultant  velocity  is  repre- 
sented by  the  diagonal  of  the  rectangle  whose  sides  are  pro- 
portional to  the  two  constituent  velocities. 

The  Parallelogram  Law. — If  a  particle  at  a,  Fig.  14, 
have  two  simultaneous  velocities  in  the  directions  of 
and  respectively  proportional  to  ab  and  acy  then  the 
position  of  the  particle  at  the  end  of  one  second  will 
be  the  same  as  if  ab  had  acted  for  one  second  carrying 
it  to  b,  and  a  velocity  bd,  parallel  and  equal  to  ac,  had 
acted  upon  it  for  the  following  second,  thus  carrying 
it  to  d.  If  the  two  velocities  act  simultaneously,  its 
path  will  accordingly  be  the  straight  line  ad,  represent- 


SQ  PHYSICS 

ing  the  diagonal  of  the  parallelogram  of  which  ab  and 
ac  are  two  adjacent  sides. 

We  may  accordingly  state  the  following  law  for  the 


composition  of  two  simultaneous  velocities  given  to  the 
same  particle: 

If  a  particle  possess  at  the  same  time  two  velocities, 
and  if  these  velocities  be  represented  by  lines  drawn  from 
the  same  point  and  forming  two  adjacent  sides  of  a 
parallelogram,  the  residtant  velocity  will  be  represented 
by  that  diagonal  of  the  parallelogram  which  is  drawn 
from  the  point  of  intersection  of  the  two  lines. 

The  Triangle  Law. — If  two  velocities  be  represented 
by  two  sides  of  a  triangle  taken  in  order,  their  residtant 
may  be  represented  by  the  third  side.  This  law  follows 
at  once  from  the  argument  used  in  developing  the 
parallelogram  law.  It  will  also  be  seen  from  the  figure 
that  it  is  immaterial  whether  the  two  velocities  are 
represented  by  ab  and  bd,  or  by  ac  and  cd,  the  resultant 
being  in  both  cases  represented  by  ad. 

Composition  of  More  than  Two  Velocities. — To  find 
the  resultant  of  more  than  two  velocities  acting  at  the 
same  time  on  a  given  particle,  find  the  resultant  of  any 
two  velocities,  then  of  this  resultant  and  a  third  velocity, 
and  continue  in  this  manner  until  all  the  velocities  have 
been  used.  The  last  resultant  will  be  the  one  sought. 


MECHANICS  51 

^Composition  of  Forces. 

LABORATORY  EXERCISE  20. — Two  spring  balances  are 
attached  by  their  hooks  to  the  ends  of  a  strong  cord  50  or 
60  centimeters  long.  The  rings  of  the  balances  are  tied  by 
pieces  of  cord  to  two  nails  or  pegs  driven  into  a  convenient 
board  or  a  table  at  a  distance  apart  about  equal  to  the  length 
of  the  string  connecting  the  balance  hooks.  A  third  balance 
is  attached  in  the  same  way  to  a  cord  about  half  as  long  as 
the  one  connecting  the  two  other  balances,  and  the  end  of 
this  cord  is  provided  with  a  loop  which  is  slipped  over  the 
longer  cord.  When  the  cords  are  pulled  straight,  the 
balances  should  lie  in  a  position  similar  to  that  shown  in 
the  figure.* 

By  means  of  a  cord  tied  to  the  ring  of  the  third  balance, 
draw  it  out  until  it  indicates  a  conveniently  large  reading, 
and  tie  it  to  another  nail  or  peg.  Tap  the  balances  and 
cords  until  the  loop  has  taken  its  position  of  equilibrium  and 
the  pointers  indicate  the  true  pull  upon  each  balance.  Place 
a  sheet  of  paper  with  its  center  under  the  intersection  of  the 
cords,  and  indicate  the  position  of  this  point  of  intersection 
by  a  dot  on  the  paper,  then  laying  a  ruler  carefully  alongside 
the  cord,  indicate  very  accurately  by  dotted  lines  the  direc- 
tion of  each  cord  from  the  point  of  intersection. 

Remove  the  paper,  and  draw  in  full  the  lines  indicating 
the  directions  of  the  cords,  and  produce  each  by  dotted  lines 
on  the  other  side  of  the  intersection.  Select  some  convenient 
scale  of  length,  as  inches  or  centimeters,  to  represent  the 
pull  on  the  balances  (thus  a  distance  of  10  centimeters  may 
represent  a  pull  of  10  ounces,  and  the  like),  and  lay  off  on 
each  line  a  distance  representing  the  pull  on  the  correspond- 
ing string.  Complete  the  parallelograms  on  each  pair  of  lines 
thus  laid  off. 

Do  the  dotted  lines  previously  drawn  become  diagonals  of 
these  parallelograms  ? 

The  resultant  of  each  pair  of  forces  must  be  always  equal 
and  opposite  to  the  third  force  by  which  it  is  balanced ;  are 
these  resultants  represented  by  the  diagonals  of  the  parallelo- 
grams which  you  have  drawn  ? 

*The  three  balances  used  in  these  experiments  may,  if  desired,  be 
replaced  by  three  suitable  weights  attached  to  cords  and  suspended  over 
two  fixed  pulleys. 


PHYSICS 


FIG.  15. 


MECHANICS 


53 


Repeat  with  the  balance  cords  attached  to  different  nails. 
Does  the  parallelogram  law  apply  to  forces  as  well  as  to 
velocities  ? 

Resolution  of  Forces,  Velocities,  and  Accelerations. 

— Any  force  or  velocity  or  acceleration  may  be  regarded 
as  the  resultant  of  two  or  more  other  forces,  velocities, 
or  accelerations.  When  the  directions  of  these  com- 
ponents are  known,  their  magnitude  may  be  calculated 
from  the  parallelogram  law. 

Thus,  let  a  represent  a  sphere  resting  upon  an 
inclined  plane.  The  force  acting  upon  the  sphere  is 


FIG.  16. 

its  weight,  and  the  direction  of  this  force  is  a  vertical 
line.  The  sphere  does  not  fall  in  a  vertical  line,  but 
it  rolls  down  the  plane  and  at  the  same  time  presses 
upon  the  plane.  The  force  by  which  it  is  impelled 
along  the  plane  and  the  force  of  its  pressure  upon  the 
plane  are  the  two  components  of  which  the  weight  of 
the  body  may  be  considered  the  resultant.  The  direc- 


54  PHYSICS 

tion  of  each  of  these  forces  is  known.  One  is  parallel 
to  the  plane,  and  the  other,  the  pressure  upon  the 
plane,  is  perpendicular  to  the  plane.  The  directions. 
of  these  forces  are  then  represented  by  the  dotted  lines, 
ac  and  ad.  If  the  direction  and  magnitude  of  the 
weight  of  the  sphere  be  represented  by  the  line  ab,  then 
is  ab  the  diagonal  of  a  parallelogram  two  of  whose 
sides  lie  in  the  lines  ac  and  ad.  Completing  this 
parallelogram,  we  find  the  magnitudes  of  the  two  com- 
ponent forces  represented  by  ac'  and  ad' . 

PROBLEMS. — Prove  geometrically  that  the  force  ac',  which 
causes  the  motion  of  the  sphere  down  the  plane,  is  to  the 
weight  of  the  sphere  as  the  height  of  the  plane  is  to  the 
length  of  the  plane. 

Referring  to  Exercise  6,  on  the  inclined  plane,  by  what 
was  the  force  ac'  represented  ? 

A  plank  10  feet  long  rests  with  one  end  on  the  ground 
and  the  other  on  a  support  6  feet  high.  A  barrel  weighing 
200  pounds  is  allowed  to  roll  down  the  plank;  what  pressure 
does  the  plank  support  ? 

If  the  plank  can  support  a  pressure  of  800  pounds,  what 
load  may  be  rolled  down  it  ? 

The  length  of  an  inclined  plane  is  to  its  height  as  4  to  i. 
What  velocity  would  a  ball  acquire  in  rolling  freely  down 
this  plane  for  one  second  ? 

RESOLUTION   OF   CIRCULAR   MOTION 

Circular  Motion  a  Resultant  Motion. — We  have 
already  assumed  (see  foot-note  on  page  37)  that  motion 
in  a  circle  can  be  resolved  into  a  uniform  rectilinear 
motion  tangent  to  the  circumference  and  an  accelera- 
tion toward  the  center  of  the  circle.  Thus,  if  the 
particle  a  (Fig.  17)  be  moving  with  the  velocity  ab 
around  c  as  a  center,  its  motion  along  ab  may  be  re- 
garded as  the  resultant  of  the  uniform  motion  ad  and 
an  acceleration  which  will  carry  it  toward  the  center  a 


MECHANICS 


55 


a 


FIG.  17. 


distance  ae   in   one  second.      Since  the   space  passed 

through  in  one  second  under  the  action 

of  a  constant  force  is  numerically  equal 

to    one     half  the    acceleration    which 

measures  the  force,  the  acceleration  of 

a  toward  c  is  equal  to  2ae. 

We  know  that  ae  is  an  acceleration, 
and  not  a  uniform  motion,  because  the 
resultant  of  two  uniform  rectilinear  mo- 
tions is  also  a  uniform  rectilinear  motion. 

We  know  that  this  acceleration  is 
always  toward  the  center  of  the  circle 
and  hence  at  right  angles  to  the  uni- 
form rectilinear  motion  of  the  particle,  as  otherwise  it 
could  be  resolved  into  two  components  one  of  which 
would  be  parallel  to  the  uniform  motion  and  would 
accordingly  accelerate  this  motion  and  with  it  the 
motion  of  the  particle  in  its  circular  path. 

We  now  wish  to  find  how  this  acceleration  varies  with 
the  speed  of  the  particle  and  with  the  radius  of  the 
circle. 

If  the  arc  ab  be  taken  so  small  that  it  does  not  differ 
perceptibly  from  a  straight  line,  then  we  know  from 
geometry  that  the  angle  abn  will  be  a  right  angle,  and 
that  we  can  make  the  proportion  ae  :  ab  =  ab  :  an, 
and  accordingly  that  ae  X  an  =  a&. 

Equation  for  the  Acceleration  Component. — Letting 
a'  =  2ae  (the  acceleration  of  the  particle  toward  the 
center  of  its  orbit),  v  =  ab  (the  orbital  velocity  of  the 
particle)  and  r  —  ac  (the  radius  of  the  circular  orbit), 
and  substituting  these  values  in  the  equation  ae  X  an  = 

atf,    we   have   a'r  =  vz,    and    a'  —  — .     Consequently 


56  PHYSICS 

when  a  particle  moves  with  uniform  velocity  in  a  cir- 
cular path  it  has  an  acceleration  toward  the  center  of 
its  orbit  which  varies  directly  as  the  square  of  the 
orbital  velocity  of  the  particle  and  inversely  as  the 
radius  of  the  circle. 

Centripetal  Force.  —  The  force  which  is  assumed  as 
the  cause  of  the  acceleration  of  the  particle  toward  the 
center  of  its  orbit  is  called  the  Centripetal  Force  of  the 
particle.  If  the  centripetal  force  ceases  to  act,  the 
particle  will  at  once  leave  its  circular  path  and  will 
continue  with  a  uniform  rectilinear  velocity  in  the 
direction  in  which  it  was  going  when  the  centripetal 
force  ceased.  If  the  centripetal  force  be  increased,  its 
orbital  velocity  will  be  increased  or  its  orbital  radius 
diminished,  or  both.  The  centripetal  force,  like  any 
other  force,  is  measured  by  the  formula  F  =  ma,  that  is, 
by  the  mass  of  the  moving  particle  times  its  accelera- 
tion toward  the  center  of  its  orbit.  Substituting  for  a 
its  value  as  determined  in  the  previous  equation,  we 


have  F  =  -  —  ,   which  is   the   equation  for  centripetal 

force. 

Centrifugal  Force.  —  The  resistance  which  the  mov- 
ing particle  offers  to  change  of  direction  of  motion  is 
often  called  the  Centrifugal  Force  of  the  body.  Used 
in  this  sense,  the  centrifugal  force  is  always  equal  in 
magnitude  and  opposite  in  direction  to  the  centripetal 
force.  This  is,  however,  an  incorrect  use  of  the  term 
force.  A  force  is  whatever  produces  or  tends  to  pro- 
duce an  acceleration,  and  the  particle  has  no  accelera- 
tion or  tendency  to  acceleration  away  from  the  center 
of  its  orbit.  The  particles  of  mud  do  not  fly  from  a 
wheel  because  they  are  pulled  off  by  a  centrifugal  force, 


MECHANICS  57 

but  because  their  attachment  to  the  wheel  is  not  strong 
enough  to  serve  as  the  centripetal  force  necessary  to 
their  rapid  circular  motion.  The  stone  in  the  sling 
does  not  pull  upon  the  string  because  it  has  a  force 
acting  upon  it  to  drive  it  away  from  the  hand,  but  the 
hand,  by  means  of  the  string,  is  constantly  pulling  it 
out  of  its  rectilinear  path. 

Since  the  attraction  between  the  particles  of  a  liquid 
is  not  great  enough  to  serve  as  a  centripetal  force  in 
the  case  of  rapid  rotation,  liquid  particles  are  always 
thrown  from  the  surface  of  a  rapidly  rotating  body. 
This  principle  is  often  applied  to  the  separation  of  liquids 
from  solids.  Thus  in  the  centrifugal  drying-machines 
used  in  laundries  the  wet  clothes  are  placed  in  metal 
cylinders  with  perforated  sides  which  are  set  in  rapid 
rotation.  The  attraction  between  the  particles  of  water 
in  the  cloth  is  not  great  enough  to  keep  the  water 
moving  in  the  circular  path,  and  it  accordingly  sepa- 
rates from  the  cloth  and  escapes  through  the  perfora- 
tions in  the  walls  of  the  cylinder. 

We  have  seen  that  the  centripetal  force  increases  as 
the  mass  of  the  rotating  particle  increases,  hence  when 
different  liquids  are  mixed  and  set  in  rotation  the 
heavier  particles,  which  are  held  to  the  liquid  mass  by 
the  same  force  as  the  lighter  particles,  sooner  escape 
to  the  surface  and  gather  on  the  walls  of  the  containing 
vessel,  while  the  lighter  liquid  is  thus  pressed  toward 
the  center  of  the  rotating  mass.  This  is  seen  in  the 
hollow  sphere  containing  mercury  and  water  which  is 
often  attached  to  the  rotating  axis  of  a  whirling  table. 
When  at  rest,  the  mercury  rests  upon  the  bottom  of 
the  vessel  and  the  water  rests  upon  the  mercury. 
When  set  in  rotation,  the  mercury  gathers  in  a  liquid 


58  PHYSICS 

band  around   the   walls   of  the  hollow  sphere  at  the 
greatest  possible  distance  from  the  axis  of  rotation. 

This  principle  is  often  applied  to  the  separation  of  a 
lighter  liquid  from  a  heavier,  as  in  the  centrifugal  cream- 
separator.  In  this  instrument  the  fresh  milk  is  allowed 
to  flow  into  a  rapidly  revolving  vessel,  the  skim-milk 
separates  from  the  cream  and  gathers  on  the  outside, 
while  the  cream  is  pressed  to  the  inside  of  the  liquid 
mass,  and  each  is  drawn  off  into,  a  suitable  receptacle. 

PROBLEMS  IN  CIRCULAR  MOTION. — A  stone  in  a  sling  is 
swung  around  the  hand  once  a  second,  and  the  pull  upon  the 
string  is  1 6  poundals.  With  what  force  must  the  string  be 
pulled  to  cause  the  stone  to  swing  around  once  in  half  a 
second  ?  Once  in  two  seconds  ? 

A  stone  weighing  two  pounds  is  attached  to  a  string  two 
feet  long  and  is  swung  around  the  hand  once  a  second. 
With  what  force  in  poundals  does  it  pull  upon  the  string  ? 

(Solution  : 

v  =  2  nr  =  4  7t  feet  per  second ; 

2 

a  =  —  =  8;r2  feet  per  second. 

A  poundal  will  give  to  one  pound  an  acceleration  of  one 
foot  per  second,  hence  to  give  to  2  pounds  an  acceleration 
of  87T2  feet  per  second  will  require  i67T2  =  157.92  poundals, 

or  F=  —  -  =  i6?r2  —  157.92.) 

A  mass  of  one  kilogram  on  a  radius  of  one  meter  makes 
one  revolution  per  second;  what  is  its  centripetal  force  in 
dynes  ? 

The  rim  of  a  fly  wheel  weighs  1000  pounds.  Its  radius 
is  5  feet.  What  centripetal  force  must  be  exerted  by  the 
spokes  when  the  wheel  makes  100  revolutions  a  minute  ? 


PART  II 

PROPERTIES   OF  BODIES 

STATES   OF   AGGREGATION 

Three  Kinds  of  Bodies. — Material  bodies  exist  in 
three  different  conditions  or  states  of  aggregation,  the 
Solid,  Liquid,  and  Gaseous  states. 

ELASTICITY 

Definition  of  Elasticity. — That  property  of  material 
bodies  which  determines  the  state  of  aggregation  in 
which  a  body  shall  exist  at  a  given  time  is  called 
Elasticity.  Elasticity  may  be  defined  as  that  property 
of  bodies  by  virtue  of  which  they  resist  a  change  of  form 
or  a  change  of  volume.  The  measure  of  elasticity  is 
the  measure  of  the  force  which  is  required  to  maintain 
a  given  change  of  form  or  change  of  volume  in  the  body 
under  consideration.  Thus  the  elasticity  of  a  bent 
spring  is  measured  by  the  force  which  is  required  to 
hold  it  bent  in  a  fixed  position;  the  elasticity  of  a 
rubber  band  is  measured  by  the  force  required  to  stretch 
it  to  a  given  length ;  the  elasticity  of  the  air  in  a  bicycle 
tire  or  a  football  is  measured  by  the  pressure  which  it 
exerts  upon  the  enclosing  walls.  Elasticity,  quantita- 
tively considered,  is,  accordingly,  the  resistance  which 
a  body  offers  to  change  of  form  or  change  of  volume. 

59 


6o  PHYSICS 

Perfect  Elasticity. — Elastic  bodies  in  which  a  given 
force  is  always  required  to  maintain  the  same  change 
of  form  or  change  of  volume  are  said  to  have  complete 
or  perfect  elasticity.  Bodies  which  lose  a  part  of  their 
elasticity  after  being  compressed  or  bent  for  a  time  are 
imperfectly  elastic. 

Rigidity. — The  resistance  which  bodies  offer  to 
change  of  form  is  also  called  Rigidity,  and  a  body 
which  possesses  rigidity  is  called  a  rigid  body,  or  a 
solid. 

Fluids. — Bodies  which  do  not  possess  sufficient 
elasticity  of  form  to  enable  them  to  retain  their  shape 
while  supporting  the  pressure  of  their  own  weight  are 
called  Fluids.  Such  bodies  spread  out  under  the 
pressure  of  their  own  weight  into  thin  layers,  or  take 
the  shape  of  the  containing  vessel. 

Two  Classes  of  Fluids. — Fluids  are  divided  into  two 
classes,  Liquids  and  Gases.  Liquids  have  very  little 
elasticity  of  form,  but  great  elasticity  of  volume;  that 
is,  they  offer  great  resistance  to  compression.  Gases 
have  no  elasticity  of  form,  and  only  relatively  slight 
elasticity  of  volume. 

Simplicity  of  Gaseous  State. — Of  these  three  states 
of  aggregation,  the  gaseous  state  is  much  the  simplest 
in  its  physical  properties,  hence  we  will  consider  it 
first. 

GASEOUS    STATE 
W  PROPERTIES   OF  GASES 

Indefinite  Expansion. — A  gaseous  body,  if  not  acted 
upon  by  any  restraining  pressure,  will  expand  indefi- 
nitely, hence  gases  always  occupy  the  entire  volume  of 


PROPERTIES  OF  BODIES 


61 


the  containing  vessel  and  exert  pressure  upon  its  walls. 
This  pressure  is  the  measure  of  the  elasticity  of  volume 
of  the  gas.  It  increases  with  the  amount  of  gas 
enclosed  in  the  containing  vessel.  Thus  when  the  tire 
of  a  bicycle  is  open  to  the  air  the  gas  contained  in  it 
exerts  no  more  pressure  upon  its  walls  than  does  the 
air  outside.  It  is  possible,  however,  by  means  of  the 
inflating  pump  to  force  enough  air  into  the  tube  to  exert 
a  great  pressure  upon  its  walls,  so  that  the  tire  remains 
distended  under  the  weight  of  the  rider. 

The  Air  Pump. — The  property  of  indefinite  expan- 
sion of  a  gas  is  made  use  of  in  the  construction  of  the 


a 


FIG.  18. 

air  pump.  This  instrument  was  invented  by  Otto  von 
Guericke,  of  Magdeburg,  about  1654,  and  in  its  orig- 
inal form  is  represented  in  the  accompanying  figure. 
A  is  the  glass  balloon  or  receiver  from  which  the  air  is 
to  be  exhausted.  B  is  a  metal  cylinder  provided  with 


62 


PHYSICS 


a  tight-fitting  piston,  P\   C  is  a  stop-cock;  and  D  is  a 
valve  opening  outward. 

To  exhaust  the  air  from  A,  the  stop-cock  C  is 
closed,  thus  shutting  off  communication  between  A  and 
B,  and  the  piston  is  pressed  down  in  the  cylinder  B. 
The  valve  at  D  is  opened  by  the  pressure  of  the  com- 
pressed air,  and  part  of  the  air  escapes.  The  stop-cock 
C  is  then  opened  and  the  piston  is  withdrawn  to  the 
end  of  the  cylinder.  The  air  in  A  expands,  filling 
both  A  and  B.  C  is  again  closed  and  P  is  pushed 
inward,  forcing  another  portion  of  the  air  out  through  D. 
This  process  is  continued  as  long  as  the  air  inside  the 
cylinder  can  be  made  to  exert  sufficient  pressure  to 
open  D. 

By  means  of  this  crude  instrument  von  Gruericke  was 
able  to  perform  many  noted  experiments  on  the  pres- 
sure of  gases.  Later,  the  instrument  was  improved  by 


FIG.  19. 

dispensing  with  the  valve  D  and  making  C  a  three-way 
cock  which  could  be  turned  so  as  to  bring  B  in  com- 
munication alternately  with  A  and  with  the  outside  air. 
Then  by  placing  C  very  near  the  cylinder  nearly  all 
the  air  on  the  side  of  C  next  to  the  cylinder  could  be 
forced  out  by  the  piston. 

A  common  form  of  the  air  pump  used  at  the  present 
time  is  made  by  placing  a  valve  B,  opening  toward  the 


PROPERTIES  OF  BODIES  63 

cylinder,  between  the  cylinder  and  receiver,  and  an- 
other valve,  C,  opening  outward  in  the  piston  as  shown 
in  Fig.  19. 

How  would  such  a  pump  need  to  be  modified  to  enable  it 
to  be  used  as  a  compression  pump  for  inflating  bicycle  tires  ? 
Explain  the  construction  of  a  bicycle  pump. 

Weight  of  Air. 

LABORATORY  EXERCISE  21. — The  weight  of  a  known  volume 
of  air  may  be  determined  in  the  following  manner: 

A  strong  glass  bottle  holding  a  liter  or  more  should  be 
fitted  air-tight  with  a  one-hole  rubber  stopper,  through  which 
a  short  glass  tube  should  pass  into  the  bottle  and  project 
four  or  five  centimeters  beyond  the  stopper  on  the  outside. 
To  make  the  joints  about  the  glass  tube  and  the  stopper  air- 
tight, it  may  be  necessary  to  pour  melted  beeswax  or  paraffin 
around  them  while  the  air  is  partly  exhausted  from  the  bottle 
so  that  the  melted  wax  will  be  forced  into  any  leaks  by  the 
pressure  of  the  air  on  the  outside.  A  piece  of  strong-walled 
but  flexible  rubber  tubing  should  be  placed  over  the  glass 
tube,  also  making  an  air-tight  joint,  and  this  should  project 
four  or  five  centimeters  beyond  the  glass  tube  and  should  be 
provided  with  a  screw  pinch-cock. 

Place  the  bottle  with  the  tube  open  and  the  pinch-cock 
upon  one  pan  of  the  platform  balance  and  carefully  counter- 
poise it  with  shot  or  other  heavy  substances  placed  on  the 
other  pan.  Then  remove  the  bottle  from  the  balance  and 
attach  the  rubber  tube  to  the  air  pump,  slipping  the  rubber 
tube  on  so  far  that  it  will  not  collapse  when  the  air  is 
exhausted,  and  exhaust  as  much  as  possible  of  the  air. 
Close  the  pinch-cock  as  near  as  possible  to  the  glass  tube, 
and  remove  from  the  air  pump  and  place  again  on  the 
balance  with  the  counterpoise  previously  used.  Add  enough 
known  weights  to  produce  equilibrium.  These  weights 
represent  the  weight  of  the  air  which  has  been  removed  from 
the  bottle. 

To  find  the  volume  of  air  which  was  removed,  squeeze  the 
air  out  of  the  open  end  of  the  rubber  tube  and  immerse  the 
tube  and  the  neck  of  the  bottle  in  a  large  vessel  of  water  and 
remove  the  pinch-cock.  Do  not  let  any  air  enter  the  bottle 
with  the  water.  When  the  water  has  ceased  flowing  into  the 


64  PHYSICS 

bottle,  lower  it  in  the  water  until  the  water  is  at  the  same 
height  inside  and  outside  the  bottle,  then  replace  the  pinch- 
cock  and  remove  from  the  water.  Pour  the  water  out  of  the 
bottle  into  a  graduated  vessel  and  measure  its  volume.  This 
will  give  you  the  volume  of  the  exhausted  air.  Record  the 
temperature  of  the  air  in  the  room  at  the  time  of  your  ex- 
periment. 

PROBLEMS. — Calculate  the  weight  of  one  cubic  centimeter 
of  air.  Of  one  liter.  Of  one  cubic  meter. 

Measure  the  dimensions  of  your  laboratory  in  meters  and 
calculate  the  weight  of  the  air  it  contains. 

Density  of  Air. — The  density  of  a  body  in  the 
C.G.S.  system  is  its  mass  in  grams  per  cubic  centi- 
meter. 

What  is  the  density  of  air  from  your  determinations  ? 
What  is  it  from  the  tables  ?  What  volume  of  air  corresponds 
to  the  smallest  weight  indicated  on  your  balance  scale  ? 
Why  should  you  use  a  large  bottle  in  the  preceding  experi- 
ment ? 

Specific  Gravity  of  Gases. — The  Specific  Gravity  of 
a  body  is  the  ratio  of  its  weight  to  the  weight  of  an 
equal  volume  of  some  other  body  chosen  as  a  standard, 
or,  in  other  words,  it  is  the  ratio  of  the  density  of  the 
body  to  the  density  of  the  standard  body.  The  specific 
gravity  of  gases  is  generally  determined  with  reference 
to  air  as  a  standard.  Thus  carbon  dioxide  is  about 
i .  5  times  as  heavy  as  air,  consequently  its  specific 
gravity  referred  to  air  is  about  1.5. 

To  Find  the  Specific  Gravity  of  Illuminating  Gas.* 

LABORATORY  EXERCISE  22. — After  carefully  drying  the 
bottle  used  in  the  preceding  experiment  place  it  upon  the 
balance  pan  and  counterpoise  as  before.  Exhaust  a  part  of 
the  air  and  determine  its  weight  as  before. 

Open  a  gas-cock  for  an  instant  to  expel  the  air,  and  after 

*  Any  gas  contained  in  a  receiver  under  a  pressure  slightly  greater 
than  the  pressure  of  the  air  may  be  used  in  this  experiment. 


PROPERTIES  OF  BODIES  65 

carefully  squeezing  the  air  out  of  the  open  end  of  the  rubber 
tube  on  the  bottle,  slip  this  over  the  tube  of  the  gas-cock. 
Turn  on  the  gas  and  remove  the  pinch-cock  from  the  rubber 
tube,  thus  filling  the  bottle  with  the  gas.  As  the  gas  is 
forced  in  under  a  pressure  slightly  greater  than  that  of  the 
outside  air,  remove  the  rubber  tube  from  the  gas-cock  for  a 
moment  before  closing  it  with  the  pinch-cock.  This  will 
allow  the  gas  on  the  inside  of  the  bottle  to  come  to  the  same 
pressure  as  the  outside  air.  After  closing  the  pinch-cock, 
return  the  bottle  to  the  balance  and  weigh  again. 

Call  the  weight  of  the  exhausted  air  wlt  and  the  weight 
necessary  to  produce  equilibrium  after  the  gas  is  in  the 
bottle  w2.  If  the  gas  is  heavier  than  air,  w2  will  have  to  be 
added  to  the  side  of  the  counterpoise.  Note  that  in  this 
case  the  weight  of  the  gas  in  the  bottle  is  wl  -j-  w3.  If  w2 
be  added  to  the  side  of  the  bottle,  it  tells  how  much  lighter 
the  gas  is  than  the  exhausted  air,  hence  the  weight  of  the 
gas  is  w1  —  w2. 

Since  the  volume  of  the  gas  is  the  same  as  the  volume  of 
air  which  it  replaces,  the  weight  of  the  gas  divided  by  the 
weight  of  the  exhausted  air  is  the  specific  gravity  of  the  gas 
as  compared  with  air.  If  the  gas  is  heavier  than  air,  its 
specific  gravity  is  accordingly  given  by  the  equation 

sp.  g.  =  —  --  ?;    if    lighter    than    air,    by   the    equation 


.          . 

sp-  g-  -;-* 

What  is  the  specific  gravity  of  the  gas  from  your  experi- 
ment ? 

If  the  density  of  air  be  taken  as  .0012,  what  is  the  density 
of  the  gas  ? 

The  density  of  hydrogen  is  .0000895;  what  is  its  specific 
gravity  referred  to  air  of  density  .0012  ? 

Pressure  of  the  Atmosphere.—  We  have  seen  that 
air  has  weight,  and  that  the  air  in  an  ordinary  school- 
room weighs  several  hundred  pounds.  We  know  also 
that  the  air  extends  to  a  great  height  above  us,  and 
that  consequently  it  must  exert  a  great  pressure  upon 
all  bodies  with  which  it  comes  in  contact. 


66 


PHYSICS 


To  Show  the  Pressure  of  the  Atmosphere. 

LABORATORY  EXERCISE  23. — Take  an  open  glass  tube  bent 
as  shown  in  Fig.  20,  the  short  arm  of  which  is  about  six 
inches  long,  and  fill  it  with  water  to  within  about  an  inch 


FIG.  20. 


FIG.  21. 


of  the  top  of  the  short  arm,  then  place  the  end  of  the  long 
arm  in  the  mouth  and  draw  out  part  of  the  air.  The  water 
rises  in  the  long  arm.  Now  incline  the  tube  until  the  water 
\ust  comes  to  the  top  of  the  short  arm,  and  holding  the 


PROPERTIES  OF  BODIES  67 

thumb  tightly  on  this  end  of  the  tube,  again  exhaust  as 
much  as  possible  of  the  air  from  the  long  arm.  Does  the 
water  rise  in  the  long  arm  as  before  ?  What  conditions  in 
the  second  experiment  are  different  from  the  first  ?  What 
apparently  forced  the  air  up  the  long  tube  in  the  first  experi- 
ment ? 

Fill  a  bottle  with  water  and  invert  it  with  its  mouth  below 
the  surface  of  water  in  another  vessel.  What  sustains  the 
column  of  water  in  the  inverted  bottle  ?  Raise  it  out  of  the 
water.  Why  does  the  water  flow  out  ? 

Completely  fill  a  drinking-glass  with  water,  cover  it  with 
a  stiff  card  in  contact  with  the  water  and,  holding  the  card 
in  place  with  the  hand,  invert  the  glass  and  remove  the  hand. 
What  holds  the  card  against  the  glass  ?  Slide  the  card  to 
one  side  and  allow  a  few  bubbles  of  air  to  enter  the  glass. 
Why  does  the  card  fall  ? 

Plug  the  stem  of  a  funnel  with  a  cork  or  piece  of  wood, 
leaving  only  a  small  hole  for  the  escape  of  the  liquid.  Sup- 
port the  funnel  on  a  ring,  fill  a  large  bottle  or  flask  with 
water  and  invert  it  with  its  mouth  in  the  funnel,  as  shown 
in  Fig.  21.  At  first  the  water  flows  out  of  the  bottle  into 
the  funnel  faster  than  it  can  flow  out  of  the  funnel.  Why 
does  not  the  funnel  overflow  ?  At  what  level  does  the  water 
come  to  rest  in  the  funnel  ?  Why  ?  When  does  more  water 
flow  out  of  the  bottle  ?  Why  ? 

The  student-lamp  is  constructed  on  the  principle  used  in 
this  apparatus.  Its  purpose  is  to  maintain  a  constant  height 
of  oil  about  the  wick. 

Measurement  of  Atmospheric  Pressure. 

LABORATORY  EXERCISE  24. — A  glass  tube  about  one  meter 
long  and  of  about  one  centimeter  internal  diameter  should 
be  closed  at  one  end  by  sealing  off  in  a  flame.  Fill  this 
tube  completely  with  clean,  dry  mercury,  and  holding  the 
thumb  tightly  over  the  open  so  as  to  exclude  all  air,  invert 
the  tube  and  place  the  open  end  beneath  the  surface  of 
mercury  in  a  convenient  vessel  and  remove  the  thumb.* 

*  All  experiments  with  mercury  should  be  performed  over  a  vessel  ar- 
ranged to  catch  any  mercury  that  is  spilled.  A  tin  or  brass  vessel  should 
not  be  used,  but  an  iron  baking  pan  is  well  adapted  to  the  purpose. 

Mercury  should  not  be  put  in  thin-walled  glass  vessels,  and  should 
not  be  allowed  to  come  in  contact  with  other  metals  than  iron.  To  free 


68  PHYSICS 

What  supports  the  column  of  mercury  in  the  tube  ?  Why 
does  it  not  stand  to  the  top  of  the  tube  ?  Does  raising  or 
lowering  the  tube  in  the  mercury  vessel  change  the  height 
of  the  column  in  the  tube  ? 

This  experiment  was  first  performed  by  Torricelli  in  1643, 
and  the  inverted  mercury  tube  came  to  be  called  Torricelli's 
Tube.  The  empty  space  at  the  top  of  the  tube  is  called  the 
Torricellian  Vacuum. 

Measure  the  height  of  the  mercury  column  in  the  tube 
above  the  mercury  in  the  vessel,  What  is  this  height  in 
centimeters  ?  In  inches  ? 

A  cubic  inch  of  mercury  weighs  approximately  half  a 
pound.  If  the  bore  of  your  tube  had  a  cross-section  of  a 
square  inch,  what  weight  of  mercury  would  be  contained  in 
the  tube  above  the  level  of  the  mercury  in  the  vessel  ?  What 
would  be  the  downward  pressure  of  this  mercury  column 
upon  a  square  inch  of  mercury  in  the  vessel  ?  What  must 
be  the  atmospheric  pressure  upon  a  square  inch  of  the 
mercury  surface  in  the  vessel  ? 

A  cubic  centimeter  of  mercury  weighs  13.6  grams.  What 
is  the  atmospheric  pressure  in  grams  per  square  centimeter 
upon  the  surface  of  the  mercury  in  the  vessel  ? 

What  depth  of  mercury  over  the  entire  surface  of  the  earth 
would  exert  a  pressure  upon  the  earth  equal  to  the  pressure 
ef  the  atmosphere  ? 

The  Barometer.* — A  Torricellian  tube  prepared  as 

it  from  grease  and  dirt,  filter  through  pin-holes  in  stiff  paper  or  squeeze 
through  chamois-skin. 

*The  instructions  generally  given  for  preparing  a  barometer  include 
the  boiling  of  the  mercury  in  the  tube  to  expel  all  the  air  and  moisture. 
This  is  a  difficult  operation  in  the  ordinary  laboratory.  A  good  barom- 
eter may  be  made  without  this  precaution  by  the  following  method: 

The  tube  should  be  of  tolerably  thick-walled  glass  with  a  bore  of  at 
least  half  a  centimeter  in  diameter.  It  should  be  carefully  cleaned  with 
water  containing  caustic  potash  or  ammonia,  then  with  water  containing 
some  nitric  acid,  and  afterward  with  pure  distilled  water.  It  should 
then  be  carefully  drained  and  dried  by  heating  in  a  tube  filled  with  sand 
pr  by  warming  the  whole  length  of  the  tube  evenly  over  a  flame.  The 
mercury  should  be  clean,  and  should  be  dried  by  heating  to  100°  C.,  or 
more. 

The  tube  should  be  placed  upright  while  warm,  and  the  hot  mercury 


PROPERTIES  OF  BODIES  69 

in  the  preceding  experiment  and  provided  with  a  scale 
for  measuring  the  height  of  the  mercury  column  is 
called  a  Barometer,  and  is  used  for  measuring  the 
atmospheric  pressure  and  for  indicating  any  changes  in 
this  pressure.  Since  the  atmospheric  pressure  at  a 
given  place  changes  with  changes  in  the  atmospheric 
conditions,  the  barometric  height  may  serve  as  an 
indication  of  these  changes. 

Since  the  pressure  due  to  the  weight  of  the  air  must 
decrease  as  we  ascend  toward  the  top  of  the  atmos- 
phere, the  barometric  height  must  decrease  as  the 
barometer  is  carried  to  higher  altitudes.  This  fact  was 
first  discovered  by  Pascal,  and  it  is  now  extensively 
used  in  measuring  the  heights  of  mountains. 

Two  principal  forms  of  the  mercury  barometer  are 
used,  the  one  used  in  our  experiment,  called  the  Cistern 
Barometer  because  the  open  end  of  the  tube  dips 
into  a  cistern  of  mercury,  and  the  other,  called  the 
Siphon  Barometer,  in  which  the  open  end  of  the  tube 
is  bent  upward  like  the  letter  J  and  is  left  open  to  the 
air.  This  form  is  shown  in  Fig.  22.  The  pressure  of 

should  be  poured  in  through  a  funnel  until  the  tube  is  filled  to  within 
two  or  three  centimeters  of  the  top.  It  should  then  be  closed  with  a 
clean  cork  and  allowed  to  stand  for  several  hours.  Several  small  air 
bubbles  will  probably  gather  on  the  glass,  and  these  must,  be  removed 
by  sweeping  them  out  with  a  large  air  bubble.  To  accomplish  this, 
hold  the  cork  in  place  with  the  thumb  and  invert  the  tube  slowly,  allow- 
ing the  air  in  the  tube  to  flow  in  the  form  of  a  large  bubble  along  the 
upper  side  of  the  tube,  sweeping  out  the  smaller  bubbles.  Repeat  this 
process  until  all  the  visible  bubbles  have  been  removed,  and  allow  the 
tube  to  stand  for  several  hours  again.  If  other  bubbles  appear,  remove 
them  as  before.  When  free  from  air,  fill  the  tube  completely  full  of 
mercury,  and  hold  a  piece  of  clean  sheet  rubber  tightly  against  the  end 
with  the  thumb  while  inverting  the  tube  in  the  cistern.  Great  care  must 
be  taken  not  to  allow  any  air  to  enter  while  the  tube  is  being  inverted 
and  opened. 


70  PHYSICS 

the  air  upon  the  mercury  in  the  open  arm  then  sup- 
ports the  mercury  column  in  the  closed  arm.  Both 
forms  were  invented  by  Torricelli.  The 
method  of  measuring  the  atmospheric 
pressure  is  the  same  in  both  forms. 

Since  the  volume  and  density  of  a  gas 
vary  with  the  pressure  upon  it,  it  is  cus- 
tomary to  give  in  the  tables  the  volume  or 
density  under  what  is  known  as  the 
standard  atmospheric  pressure.  This 
standard  pressure  is  taken  as  the  pressure 
which  will  support  a  mercury  column  30 
inches  or  76  centimeters  high.  By  a 
pressure  of  one  atmosphere  we  accord- 
ingly mean  a  pressure  of  1033  grams  per 
square  centimeter  or,  in  round  numbers, 
15  pounds  to  the  square  inch. 

Since  a  saap  bubble  or  a  toy  balloon 
retains  the  spherical  form  under  this  great 
pressure,  the  pressure  must  be  equal  in  all 
FIG.  22.       directions.      If  the  vertical  pressure  were 
greater  than    the  horizontal,    the  bubble   or   balloon 
would  be  flattened  on  the  top  and  bottom. 

Since  a  soap  bubble  takes  the  spherical  form  while 
being  blown,  it  must  be  that  the  pressure  of  the  air 
which  is  forced  into  it  is  transmitted  uniformly  in  all 
directions. 

Atmospheric  Pressure  and  Respiration.  —  The 
process  of  respiration  in  the  animal  body  is  largely 
carried  on  by  means  of  the  atmospheric  pressure.  The 
lungs  are  elastic  bags  suspended  within  a  closed  cavity 
whose  dimensions  can  be  changed  by  the  contraction 
of  muscles  within  its  walls.  The  elastic  walls  of  the 


PROPERTIES  OF  BODIES  71 

lungs  themselves  require  but  little  pressure  to  stretch 
them  (not  more  than  a  fourth  of  a  pound  to  the  square 
inch),  consequently  the  pressure  of  the  external  air  keeps 
them  expanded,  and  causes  them  to  entirely  fill  the 
pleural  cavity  in  which  they  are  suspended,  and  to  press 
against  its  walls.  When  the  pleural  cavity  is  enlarged 
by  the  contraction  of  the  external  intercostal  muscles 
and  the  muscles  of  the  diaphragm,  more  air  is  pressed 
into  the  lungs,  causing  them  to  expand  as  the  pleural 
cavity  expands.  When  the  internal  intercostal  muscles 
contract  and  the  muscles  of  the  diaphragm  relax,  the 
walls  of  the  pleural  cavity  contract  and  compress  the 
lungs,  thus  forcing  some  of  the  air  out  of  them. 

When  we  ' '  suck  the  air  out  "  of  a  vessel  we  merely 
make  the  pressure  of  our  lungs  upon  the  enclosed  air 
less  than  the  pressure  of  the  air  in  the  vessel,  and  this 
air  expands  under  the  lessened  pressure  and  a  part  of 
it  enters  the  lungs.  We  can  accordingly  suck  only 
enough  air  out  of  a  vessel  to  make  the  pressure  of  the 
air  in  it  the  same  as  the  pressure  of  the  air  in  our  lungs. 

In  forced  inspiration  the  chest  expands  enough  to 
lower  the  pressure  of  the  air  within  the  lungs  by  about 
150.  grams  to  the  square  centimeter,  and  by  a  special 
effort  enough  air  can  be  sucked  out  of  a  tube  to  cause 
the  pressure  of  the  outside  air  to  raise  a.  column  of 
water  two  meters  or  more  in  the  tube.  That  is,  the 
pressure  of  the  air  within  the  lungs  may  be  decreased 
by  about  \  of  an  atmosphere.  X 

Pressure  of  Fluids  Within  the  Body. — Since  the 
atmosphere  exerts  a  pressure  of  15  pounds  to  the 
square  inch  upon  all  the  external  and  internal  surfaces 
of  the  body  which  open  to  the  air,  the  fluids  of  the  body 
must  exert  a  like  pressure  upon  the  walls  of  their  con- 


72  PHYSICS 

taining  vessels  to  prevent  these  walls  from  collapsing. 
If  the  external  pressure  upon  any  part  of  the  body  is 
removed,  the  internal  pressure  will  distend  the  blood- 
vessels and  other  cavities  containing  the  fluids  toward 
the  region  of  decreased  pressure. 

Experiment  with  Hand-glass. 

LABORATORY  EXERCISE  25. — Place  a  hand-glass  on  the 
plate  of  an  air  pump,  hold  the  hand  tightly  on  the  top  of  the 
glass  and  exhaust  some  of  the  air  from  the  glass.  Note  the 
feeling  and  appearance  of  the  hand,  and  explain  the  cause. 

PROBLEMS. — A  barometer  tube  is  filled  with  mercury  and 
inverted  in  a  mercury  cistern,  and  the  column  of  mercury 
stands  30  inches  high  in  the  tube.  It  is  then  pressed  down 
into  the  cistern  until  the  top  of  the  tube  is  only  20  inches 
above  the  surface  of  the  mercury  in  the  cistern ;  what  is  the 
upward  pressure  per  square  inch  of  the  mercury  column 
against  the  top  of  the  tube  ? 

What,  when  the  top  of  the  tube  is  only  10  inches  above 
the  surface  of  mercury  in  the  cistern  ? 

Is  the  external  pressure  of  the  air  upon  the  end  of  the 
tube  greater  or  less  than  the  internal  pressure  of  mercury 
against  it  ? 

•  If  the  tube  were  made  of  thin  rubber  at  the  end,  would  it 
expand  or  collapse  ? 

Two  barometer  tubes  less  than  30  inches  long  stand  side 
by  side  with  their  tops  at  the  same  level,  but  the  surface  of 
the  mercury  in  one  cistern  is  10  inches  higher  than  in  the 
other  cistern;  how  much  greater  is  the  upward  pressure  of 
the  mercury  column  in  the  shorter  tube  ? 

Two  barometers  stand  side  by  side  and  are  connected  by 
three  cross-tubes,  provided  with  stop-cocks  as  shown  in  Fig. 
23.  The  mercury  stands  30  inches  high  in  each  tube,  but 
the  surface  of  mercury  in  cistern  B  is  10  inches  higher  than 
in  cistern  A. 

Will  the  height  of  either  column  be  affected  by  opening 
cock  a,  which  is  above  the  mercury  in  both  tubes  ? 

Cock  b  is  4  inches  below  the  top  of  the  column  in  J3,  but 
above  the  top  of  the  column  in  A. 

If  b  is  opened,  mercury  will  flow  from  B  into  A.     What 


PROPERTIES  OF  BODIES 


73 


pressure  will  be  required  to  stop  this  flow  ?     How  long  will 
the  flow  continue  ? 


FIG.  23. 

If  b  is  closed  and  cock  c  is  opened,  what  pressure  will  be 
required  to  stop  the  flow  towards  A  ?  Would  this  pressure 
be  the  same,  or  different,  if  both  tubes  were  sealed  off  just 
above  the  cross-tube  c  ?  When  will  the  flow  cease  ? 


74 


PHYSICS 


A  U  tube  is  filled  with  mercury  and  inverted  with  its  ends 
in  different  vessels  of  mercury.  It  stands  with  the  top  of  its 
bend  8  inches  above  the  mercury  in  one  vessel  and  1 2  inches 
above  the  mercury  in  the  other;  will  the  mercury  flow  from 


FIG.  24. 

one   vessel    to   the  other  ?     If   so,    what   pressure  will    be 
required  to  stop  its  flow  ? 

The  Siphon. 

LABORATORY  EXERCISE  26. — Fill  all  tube  with  water  and, 
closing  the  ends,  invert  it  with  the  ends  in  two  vessels  of 
water.  Raise  one  vessel  until  the  water  is  higher  in  it  than 
in  the  other,  and  explain  what  occurs. 

Such  a  tube  is  called  a  Siphon.  It  is  often  used  to  draw 
off  liquids  from  one  vessel  into  another. 

Since  the  liquid  is  raised  in  the  siphon,  as  in  the  barom- 
eter, by  atmospheric  pressure,  the  upward  pressure  against 
the  bend  of  the  siphon  is  the  atmospheric  pressure  less  the 
weight  of  the  column  of  liquid  supported.  If  this  pressure 
is  the  same  in  both  arms  of  the  tube,  no  flow  will  take  place. 
The  pressure  which  causes  the  flow  is  the  difference  in  the 
weight  of  the  liquid  column  in  the  two  tubes. 

Can  you  raise  water  from  a  lower  to  a  higher  level  by 
means  of  a  siphon  ? 


PROPERTIES  OF  BODIES 


75 


Over  what   height   can   mercury  be   made  to   flow   in   a 
siphon  ? 

To  what  height  can  water  be  siphoned  ? 

If  a  siphon  tube  were  made  of  thin  rubber,    would   it 
expand  or  collapse  ? 

Pumps. — In  the  common  suction  pump  used  in  rais- 
ing water  a  piston  provided  with  a  valve  opening 
upward  moves  air-tight  in  a 
cylinder  at  the  bottom  of  which 
there  is  also  a  valve  opening 
upward.  When  the  piston  is 
lowered,  the  piston  valve  is 
pressed  open  by  the  confined 
air,  while  the  valve  in  the  bottom 
of  the  cylinder  is  kept  closed  by 
the  same  pressure.  The  air 
accordingly  passes  through  the 
piston  valve  above  the  piston. 
When  the  piston  comes  to  rest, 
its  valve  closes  by  its  own  weight, 
and  when  the  piston  is  raised  it 
raises  most  of  the  air  in  the  cyl- 
inder and  relieves  the  lower  valve 
of  the  downward  pressure  of  the 
atmosphere.  The  atmospheric 
pressure  upon  the  water  outside 
the  cylinder  forces  it  up  into  the 
cylinder  and  through  this  valve. 
As  the  process  is  repeated,  the  FIG.  25. 

air  is  all  drawn  out  of  the  cylinder  and  the  water  rises 
to  the  piston.  When  the  piston  is  then  forced  down, 
some  of  the  water  passes  through  the  piston  valve  and 
is  then  raised  by  the  piston  and  flows  out  through  the 
spout. 


76 


PHYSICS 


Could  such  a  pump  be  made  to  work  with  the  outflow 
spout  below  the  piston  ? 

When  the  barometer  stands  30  inches  high,  what  is  the 
maximum  height  to  which  water  can  be  raised  by  a  suction- 
pump  ? 

In  the  force  pump  the  piston  has  no  valve  and  the 
outflow  pipe  opens  into  the  cylinder  below  the  piston 
and  has  a  valve  opening  outward.  When  the  piston 
is  forced  downward  the  water  is  pressed  into  this  side 
tube  against  the  pressure  of  the  atmosphere  and  the 
weight  of  the  water  already  in  the  tube.  The  height 


FIG.  26. 

to  which  it  can  be  thus  forced  depends  only  upon  the 
pressure  which  can  be  applied  to  the  piston. 

In  marvy  pumps  of  this  class  the  water  is  forced  into 
an  air  chamber  in  which  it  compresses  the  air  and  then 
flows  out  through  a  Discharge  pipe.  The  compressed 
air  serves  to  keep  the  discharge  constant.  Fire  engines 
are  pumps  of  this  class. 


PROPERTIES  OF  BODIES 


77 


LAWS   OF   GASES 

Relation  of  Gaseous  Volume  to  Pressure. — We  have 
seen  that  a  gas  is  com- 
pressed into  a  smaller 
volume  by  an  increase  of 
the  pressure  upon  it,  but 
we  have  not  yet  seen 
how  much  the  volume  is 


changed  for  a  given  change 
of  pressure.  This  relation 
of  volume  to  pressure  was 
first  discovered  by  Robert 
Boyle  in  1662,  and  the 
method  adopted  by  him  is 
still  used  in  making  the 
same  determination. 

Boyle's  Experiment. 

LABORATORY  EXERCISE  27. 
— The  instrument  used  by 
Boyle  for  determining  the  re- 
lation between  the  volume 
and  pressure  of  a  gas,  and 
known  as  Boyle's  Tube,  is  a 
long  J  tube,  the  short  arm  of 
which  is  sealed  and  the  long 
arm  of  which  is  about  a 
meter  in  length.  If  this  form 
of  tube  is  used,  pour  enough 
mercury  in  the  open  arm  to 
just  fill  the  bend  of  the  tube, 
as  shown  in  the  figure.  By 
tilting  the  tube  and  allowing 
bubbles  of  air  to  pass  from 
one  tube  to  the  other,  the 
pressure  of  air  in  the  closed 
tube  can  be  regulated  until  FlG>  27* 

the  mercury  stands  at  exactly  the  same  height  in  both  arms  of 


110— _, 
9oJl 

70-jf 

60-4 
50_| 
40_J§ 
30_I§ 


20^1 


PHYSICS 


the  tube.  The  air  in  the  closed  tube  then  presses  upon 
the  mercury  as  much  as  the  air  in  the  open  tube.  This 
pressure  in  centimeters  or  inches  of  mercury  is  measured  by 
the  height  of  the  barometer  column  at  the  time  of  the  ex- 
periment. If  this  cannot  be  read  from  the  barometer,  it  may 
be  taken  as  it  was  determined  in  Exercise  24.  Measure  the 
length  of  the  air  column  in  the  closed  tube  as  it  stands  under 
the  pressure  of  an  atmosphere.  Call  this  length  vl}  and 
the  height  of  the  barometer  column  pr  Then  pour  mer- 
cury into  the  longer  tube  until  it  is  about  one  third  full. 
Measure  again  the  length  of  the  air  column  in  the  closed 
tube,  calling  this  length  vz,  and  measure  the  height  of  the 
mercury  in  the  open  arm  above  the  level  of  the  mercury  in 
the  closed  arm.  This  height  represents  the  additional  pres- 
sure upon  the  air  in  the  closed  tube.  Add  this  height  to  the 
height  of  the  barometer  column  to  give  the  total  pressure 
upon  the  enclosed  air,  and  call  this  pressure  p2. 

Fill  the  tube  about  two  thirds  full  of  mercury  and  deter- 
mine the  values  of  z>3  and/3. 

Now  pour  mercury  into  the 
open  tube  until  the  value  of  z>4 
is  one  half  vlt  and  find  the 
value  of  /4.*  Write  your  re- 
sults in  parallel  columns  and 
the  products  of  pl  and  vlt  p^ 
and  z>2,  etc.,  in  a  third  column 
as  indicated  in  the  diagram. 


No. 


Compare  the  results  obtained  in  the  last  column. 
Boyle's  Law. 

The  law  of  the  relation  of  volume  to  pressure  in  a  gas, 
known  as  Boyle's  Law,  is  generally  stated  as  follows:  "The 

*  An  improved  form  of  Boyle's  Tube  is  now  made  by  connecting  an 
open  and  a  closed  glass  tube  by  a  long  piece  of  strong  rubber  tubing, 
filling  the  rubber  tube  and  about  half  the  length  of  the  glass  tubes  with 
mercury  and  mounting  them  side  by  side  on  an  upright  board  so  that 
either  one  can  be  clamped  at  any  height  on  the  board.  To  bring  the 
air  in  the  closed  tube  under  atmospheric  pressure,  it  is  only  necessary  to 
make  the  height  of  the  mercury  column  the  same  in  the  open  and  the 
closed  tube.  If  this  instrument  is  used,  make  measurements  of  the  air 
column  at  less  than  atmospheric  pressure,  as  well  as  under  the  increased 
pressures  as  directed  above. 


OF 


PROPERTIES  OF  BODIES 


79 


volume  of  a  given  mass  of  gas,  kepi  at  a  given  temperature,  is 
inversely  as  the  pressure. 

Do  your  results  show  this  for  air  ? 

Stated  as  an  equation,  this  means,  The  numerical  product 
of  the  volume  into  the  pressure  of  a  given  mass  of  gas  is  a  con- 
stant; or  stated  in  algebraic  symbols,  pv  =  c. 

This  law  holds  very  approximately  for  all  gases  when  they 
are  not  compressed  into  too  small  a  volume,  and  when  they 
are  not  cooled  to  a  temperature  too  near  that  at  which  they 
condense  to  liquids. 

PROBLEMS, — What  would  be  the  length  of  the  air  column 
in  your  Boyle's  Tube  under  a  pressure  of  four  atmospheres  ? 
Under  a  pressure  of  one-fourth  atmosphere  ? 

How  could  you  measure  the  barometric  height  by  means 
of  a  Boyle's  Tube  ? 

How  does  the  density  of  a  gas  vary  with  the  pressure 
which  it  sustains  ? 

What  is  the  density  of  air  under  a 
pressure  of  10  atmospheres  ?  Under  a 
pressure  of  half  an  atmosphere  ? 

Relation  of  a  Gas  Volume  to 
Temperature. — If  a  glass  bulb  pro- 
vided with  a  stem  of  small  bore, 
or  a  bottle  with  a  glass  tube  of 
small  bore  passed  tightly  through 
its  stopper,  be  inverted  with  the 
open  end  of  the  tube  in  a  vessel 
of  water  and  the  bulb  or  bottle  be 
warmed  by  the  hand  or  otherwise, 
the  enclosed  air  will  expand  and 
some  of  it  will  bubble  up  through  the 
water.  If  the  bulb  be  now  cooled, 
the  air  in  it  will  contract  and  the 
water  will  rise  in  the  stem.  The 
volume  of  a  gas  accordingly  depends 
not  only  upon  the  pressure  which  it  supports,  but  also 
upon  its  temperature. 


FIG.  28. 


8o  PHYSICS 

Measurement  of  Heat  Expansion  of  a  Gas. 

LABORATORY  EXERCISE  28. — A  glass  tube  about  50  centi- 
meters long  and  with  a  bore  of  from  2  to  3  millimeters 
should  be  cleaned  and  dried  and  one  end  sealed  off  abruptly 
in  a  flame,  keeping  the  bore  uniform  as  near  as  possible  to 
the  closed  end  of  the  tube.  Warm  the  tube  throughout  its 
length  over  a  flame,  until  it  is  as  hot  as  it  can  be  held  in  the 
hand,  and  place  its  open  end  below  the  surface  of  mercury 
in  a  vessel  and  allow  it  to  cool  until  a  column  of  mercury 
5  or  6  centimeters  long  has  entered  the  tube;  then  place  the 
tube  upright  with  its  closed  end  down,  and  by  means  of  a 
fine  iron  wire  lower  the  mercury  column  in  the  tube  until 
the  enclosed  air  column  is  30  centimeters  or  more  in  length. 
This  can  be  done  by  pushing  the  wire  slowly  through  the 
mercury,  when  a  bubble  of  air  will  rise  along  the  wire  and 
the  mercury  will  sink  for  a  small  distance.  If  the  mercury 
breaks  up  into  separate  parts,  it  can  be  brought  together  by 
drawing  off  by  means  of  the  wire  the  air  between  the  parts. 
In  a  very  few  trials  the  mercury  can  be  placed  in  any  desired 
position. 

Make  a  mark  on  the  tube  273  millimeters*  from  the 
closed  end,  allowing  for  the  contraction  at  the  end  of  the 
tube,  and  stand  the  tube  in  a  tall  vessel  filled  with  broken 
ice  or  snow  so  that  the  enclosed  air  will  be  entirely  sur- 
rounded by  the  ice  and  water.  After  the  air  has  had  time  to 
cool  to  the  temperature  of  the  ice,  lower  the  bottom  of  the 
mercury  index  carefully  to  your  mark  and  withdraw  the  tube 
from  the  ice  and  place  it  in  a  vessel  of  hot  water,  immersing 
it  as  before  to  the  top  of  the  air  column.  When  the  mercury 
has  come  to  rest,  measure  the  temperature  of  the  hot  water 
with  a  Centigrade  thermometer,  and  measure  the  length  of 
the  column  of  enclosed  air.  The  increase  of  volume  will 
be  proportional  to  the  increase  of  length  of  the  air  column. 

By  what  length  does  the  air  column  expand  for  each 
degree  of  increase  of  temperature  ? 

By  what  part  of  its  zero  volume  does  it  expand  for  each 
degree  of  increase  of  temperature  ? 

If  its  rate  of  expansion  remains  uniform,  to  what  tempera- 
ture must  it  be  heated  to  double  its  zero  volume  ? 

*  Any  other  length  of  air  column  can  be  used  if  its  zero  length  is  care- 
fully determined. 


PROPERTIES  OF  BODIES  81 

If  its  volume  continues  to  contract  on  cooling  below  zero 
at  the  same  rate  as  above  zero,  at  what  temperature  would 
its  volume  become  zero  ? 

The  number  by  which  the  volume  of  a  gas  quantity  taken 
at  zero  temperature  must  be  multiplied  to  give  its  change 
of  volume  for  one  degree  of  temperature  is  called  its  coeffi- 
cient of  cubical  expansion.  Thus  if  VQ  represent  the  volume 
at  zero  and  b  represent  its  coefficient  of  cubical  expansion, 
its  volume  at  ten  degrees  is  vw  =  VQ(I  -|-  lob] ;  or  in  general, 
if  v  represent  the  volume  before  expansion  and  v'  the  volume 
after  expansion,  v'  =  v(i  +  3/),  where  /  expresses  the  tem- 
perature change. 

What  is  the  coefficient  of  cubical  expansion  of  air  from 
your  data  ? 

Law  of  Charles. — The  Law  of  Charles,  sometimes^ 
called  the  Law  of  Gay-Lussac,  states  that  All  gases 
expand  or  contract  by  1/273  of  their  zero  volume  for  a 
change  of  temperature  of  one  degree  Centigrade. 

The  coefficient  of  cubical  expansion  of  a  gas  is, 
therefore,  1/273. 

To  determine  this  expansion  accurately,  the  expan- 
sion of  the  containing  vessel  must  be  taken  into  con- 
sideration. 

How  great  is  the  error  of  your  determination  ?  What 
part  of  the  whole  coefficient  is  your  error  ?  What  percentage 
of  the  whole  coefficient  is  your  error  ? 

Absolute  Temperature. — The  instrument  used  by 
you  in  measuring  the  gas  expansion  may  be  regarded 
as  a  thermometer,  because  by  means  of  it  you  may 
measure  the  temperature  of  a  body  or  of  the  air.  If 
the  zero  of  temperature  correspond  with  the  zero  of 
volume,  and  if  the  Centigrade  zero  be  marked  273°  on 
your  tube,  then  the  gas  volume  will  vary  as  the  tem- 
perature varies.  That  is,  the  length  of  your  air  column 
is  273  millimeters  at  a  temperature  of  273°  on  your 


82  PHYSICS 

scale,  and  its  length  will  be  373  millimeters  at  a  tem- 
perature of  373°,  .and  so  following. 

A  gas  thermometer  so  graduated  that  the  volume  of 
the  gas  will  increase  as  the  temperature  increases  and 
decrease  as  the  temperature  decreases  is  said  to  be 
graduated  in  the  absolute  temperature  scale.  It  is 
known,  however,  that  gases  do  not  contract  according 
to  Charles'  Law  until  their  volume  disappears.  Before 
this  temperature  is  reached,  the  gas  will  become  a 
liquid,  and  its  volume  contraction  will  be  much  less. 
A  gas  thermometer  cannot  'be  used  for  measuring  tem- 
perature near  the  zero  of  the  absolute  scale. 

To  change  the  reading  of  a  Centigrade  thermometer 
to  the  absolute  scale,  we  add  273°  to  its  readings. 

Change  of  Pressure  with  Change  of  Temperature. 
— Gases  expand  according  to  the  Law  of  Charles  under 
any  ordinary  pressures,  consequently  to  maintain  the 
volume  of  a  gas  constant  while  it  is  being  heated  the 
pressure  must  be  increased.  By  heating  to  373° 
Centigrade  its  volume  is  doubled.  To  reduce  it  to  its 
original  volume,  the  pressure  must  be  doubled. 
Accordingly  the  constant  product  pv  which  you  deter- 
mined with  the  Boyle's  tube  is  only  constant  so  long 
as  the  temperature  is  constant.  Some  of  your  varia- 
tions from  Boyle's  Law  were  probably  due  to  tempera- 
ture changes  in  the  enclosed  gas  during  the  experiment. 

Since  the  product  pv  is  a  constant,  and  since  if  p 
remains  constant  v  changes  by  1/273  °f  its  zero  value 
for  every  degree  of  temperature,  it  must  be  likewise 
true  that  if  v  be  kept  constant/  must  change  by  1/273 
of  its  zero  value  for  every  degree  of  temperature. 

The  Gas  Equation. — We  may  then  combine  the  two 
statements  and  say  that  the  product  pv  changes  by 


PROPERTIES  OF  BODIES  83 

1/273  of  its  zero  value  for  every  Centigrade  degree  of 
temperature  change,  or,  if  we  use  the  absolute  scale  of 
temperature  instead  of  the  Centigrade  scale,  we  can 
say  that  pv  varies  as  the  absolute  temperature,  or  alge- 
braically pv  —  cT,  where  c  is  a  constant  factor  and  T 
is  the  absolute  temperature  of  the  gas. 

When  the  barometer  stands  76  centimeters  high  a  quantity 
of  gas  in  a  Boyle's  tube  is  warmed  from  o°  C.  to  10°  C. 
What  height  of  mercury  must  be  added  to  the  long  arm  to 
restore  the  gas  to  its  original  volume  ? 

The  value  of  the  constant  c  can  be  calculated  for  any 
given  volume  of  a  gas.  We  have  previously  seen  that 
a  gas  volume  must  always  be  measured  under  a 
standard  pressure  of  76  centimeters  or  30  inches  of 
mercury,  and  we  have  now  seen  that  the  temperature 
must  be  specified  if  different  gas  volumes  are  to  be 
comparable  with  each  other.  It  is  accordingly  cus- 
tomary to  specify  the  volume  of  a  gas  under  standard 
pressure  and  standard  temperature,  and  the  tempera- 
ture of  melting  ice,  which  is  the  Centigrade  zero  or  the 
absolute  273°,  is  taken  as  the  standard  temperature. 

PROBLEMS. — To  calculate  the  value  of  the  constant  c  for 
one  liter  of  air  under  standard  conditions  of  temperature  and 
pressure  we  proceed  as  follows: 

Our  equation  is 

pv 
pv  =  cT,     or     c=^-. 

/is  1033  grams  and  the  weight  of  one  gram  is  980  dynes; 
hence 

p  =  1033  x  980  dynes; 

v  =  1000  cubic  centimeters; 

T=  273°. 
Hence 

c  =  1033  x  98°  X  1000  -h  273  =  ? 


84  PHYSICS 

What  volume  of  air  at  20°  C.  and  under  standard  pres- 
sure is  equivalent  to  i  liter  under  standard  pressure  and 
temperature  ? 

A  liter  of  air  measured  under  standard  conditions  is  again 
measured  under  a  pressure  of  57  centimeters  and  a  tempera- 
ture of  25°  C.  What  volume  does  it  occupy  ? 

Calculate  the  value  of  the  constant  c  in  both  cases. 

Using  the  density  of  air  as  determined  in  Laboratory 
Exercise  21,  find  the  value  of  the  constant  c  for  2  grams 
of  air  under  standard  pressure  at  a  temperature  of  27°  C. 

Work  Done  by  Expanding  Gas. — We  have  seen  that 
a  volume  of  gas  kept  under  constant  pressure  will 
expand  1/273  of  its  zero  Centigrade  volume  for  one 
degree  increase  of  temperature.  Since  in  expanding 
it  must  push  back  the  outside  air,  it  must  accordingly 
do  work.  We  have  seen  that  work  is  measured  by 
the  product  of  the  force  into  the  distance,  or  W  =  FS. 
Here  the  force  is  the  pressure  in  dynes  of  the  outside 
air,  the  space  is  the  distance  through  which  this  air  is 
pressed  back  by  the  expanding  gas. 

PROBLEMS. — Suppose  a  horizontal  glass  tube  with  a  bore 
of  one  square  centimeter  cross-section  to  contain  at  o°  C. 
a  column  of  air  273  centimeters  long  which  is  separated 
from  the  outside  air  by  a  frictionless  piston.  Let  this  tube 
be  warmed  through  10°  C.  and  calculate  the  work  done  by 
the  expanding  gas. 

(The  gas  expands  and  pushes  the  index  10  centimeters 
along  the  tube.  The  pressure  is  1033  x  980  dynes.  The 
work  is  accordingly  1033  x  980  X  10  ergs.) 

Suppose  the  bore  of  the  tube  to  be  one  half  as  great  and 
the  length  of  the  air  column  to  be  twice  as  great  as  before, 
is  the  work  the  same  ?  Is  the  change  of  volume  of  the  gas 
the  same  ? 

Suppose  the  pressure  upon  the  gas  to  be  one  half  as  great. 
Its  initial  volume  will  then  be  twice  as  great  and  its  increase 
of  volume  due  to  heating  will  be  twice  as  great.  It  will 
accordingly  overcome  one  half  the  previous  pressure  through 


PROPERTIES  OF  BODIES  85 

twice  the  previous  distance  and  will  do  the  same  quantity  of 
work  as  before. 

Suppose  a  gas  under  standard  pressure  in  a  cylinder  whose 
cross-section  is  10  square  centimeters  and  let  it  expand  by 
heating  until  its  volume  is  increased  by  10  cubic  centimeters. 
How  much  work  must  it  do  ? 

If  the  volume  of  a  gas  before  expansion  is  z^,  its  volume 
after  expansion  is  v2,  and  the  pressure  in  dynes  under  which 
it  expands  is  p,  the  work  in  ergs  done  by  the  expanding  gas 
is  W  —  (v2  —  v^p.  Show  that  this  equation  applies  to  the 
preceding  problems. 

State  the  above  equation  in  words. 

A  liter  of  gas  under  standard  pressure  is  heated  from 
o°  C.  to  273°  C. ;  what  quantity  of  work  does  it  do  in 
expanding  ? 

Universality  of  Gas  Equation. — In  our  experiments 
upon  gases  thus  far  we  have  used  only  air,  and  it  would 
be  rash  to  infer  that  the  laws  relating  to  the  volume 
and  pressure  of  air  are  true  for  all  gases.  Many 
thousand  experiments  made  by  a  great  many  observers 
on  different  gases  have  shown,  however,  that  in  their 
physical  properties  all  gases  are  very  much  alike. 
They  may  differ  in  density,  in  color,  in  chemical 
properties ;  but  the  gas  laws  of  Boyle  and  Charles  apply 
with  only  slight  modifications  to  all  gases  not  near  their 
state  of  liquefaction. 

Dalton's  Law. — In  1801  John  Dalton  announced  as 
the  result  of  his  experiments  upon  a  number  of  mixed 
gases  that  "  The  total  pressure  of  a  mixture  of  gases 
equals  the  sum  of  the  pressures  of  the  individual 
gases."  That  is,  if  a  closed  vessel  contain  oxygen 
enough  to  exert  a  pressure  of  5  pounds  to  the  square 
inch  and  nitrogen  enough  to  exert  a  pressure  of  10 
pounds  to  the  square  inch  the  total  pressure  upon  the 
walls  of  the  vessel  will  be  1 5  pounds  to  the  square  inch. 


86  PHYSICS 

In  other  words,  a  gas  exerts  the  same  pressure  upon 
the  walls  of  the  containing  vessel  whether  it  occupies 
the  space  alone  or  with  another  gas. 

NATURE   OF   GASES 

All  Gases  have  Similar  Structure. — The  remark- 
able similarity  in  the  physical  properties  of  gases  has 
led  to  the  belief  that  in  their  structure  all  gases  must 
be  very  much  alike.  This  is  not  true  in  the  same  sense 
of  liquids  and  solids.  Scarcely  two  of  these  can  be 
found  which  have  the  same  expansion  coefficient  or 
which  are  affected  by  the  same  amount  for  a  given 
change  of  pressure.  They  are  accordingly  supposed 
to  be  much  more  complex  in  their  internal  structure 
than  are  gases,  and  we  regard  the  gaseous  state  of 
aggregation  as  the  simplest  condition  in  which  bodies 
are  known  to  exist. 

Two  Possible  Theories  of  Gas  Structure. — There 
are  two  possible  assumptions,  and  apparently  only  two, 
concerning  the  structure  of  gases.  One  is  that  a  gas 
is  a  continuous  substance  of  small  density  which 
expands  indefinitely  and  fills  all  the  space  at  its  dis- 
posal ;  and  the  other  is  that  a  gas  is  made  up  of  dis- 
connected particles  which  separate  as  far  as  possible 
from  each  other,  and  hence  occupy  all  the  space  at 
their  disposal. 

Comparison  of  Two  Theories.  —  Under  the  first 
assumption,  when  several  gases  fill  the  same  vessel 
their  substances  actually  interpenetrate  each  other  so 
that  any  material  point  taken  in  the  vessel  will  be  at 
the  same  time  a  part  of  all  the  gases.  Under  the 
second  assumption,  no  two  gas  particles  can  occupy 
the  same  space  at  the  same  time,  but  when  gases  mix 


PROPERTIES  OF  BODIES  87 

their  particles  are  distributed  regardless  of  orderly 
arrangement  throughout  the  entire  space  to  which  they 
are  confined. 

Molecules  and  Atoms. — From  the  fact  that  solids 
and  liquids  are  divisible  into  smaller  and  smaller 
particles  as  far  as  we  can  carry  the  division  by 
mechanical  means,  it*  seems  probable  that  the  second 
assumption  is  the  correct  one,  and  that  gases  are  made 
up  of  these  small  particles — the  very  smallest  into 
which  the  substance  can  be  divided  without  changing 
its  nature. 

Many  of  these  particles  we  know  to  be  compound. 
Thus  water  is  composed  of  hydrogen  and  oxygen .  The 
smallest  possible  water  particle  must  contain  hydrogen 
and  oxygen.  Steam,  or  water  gas,  is  supposed  to  be 
made  up  of  these  smallest  possible  water  particles, 
which  are  called  water  Molecules,  and  each  of  these  is 
supposed  to  be  composed  of  smaller  particles  of 
hydrogen  and  oxygen,  called  Atoms.  Thus,  when- 
ever a  particle  exists  by  itself  it  is  called  a  molecule ; 
when  it  is  combined  with  other  particles  to  form  a 
molecule  it  is  called  an  atom.  The  same  particle  may 
be  sometimes  an  atom  and  sometimes  a  molecule. 

Chemical  Evidence  of  Atoms  and  Molecules. — This 
theory  is  much  strengthened  by  evidence  derived  from 
chemical  reactions,  from  which  we  find  that  when  sub- 
stances combine  to  form  a  different  substance,  as 
hydrogen  and  oxygen  to  form  water,  they  always 
combine  in  definite  proportions,  and  that  only  a  small 
number  of  definite  compounds  can  be  made  from  any 
two  substances.  Thus,  two  volumes  of  hydrogen  gas 
always  combine  with  one  volume  of  oxygen  gas  to 
form  two  volumes  of  water  vapor,  three  volumes  of 


88  PHYSICS 

hydrogen  and  one  volume  of  nitrogen  to  form  two 
volumes  of  ammonia  gas,  and  the  like.  If  gases  were 
absolutely  continuous  bodies,  we  can  see  no  reason 
why  they  should  not  combine  in  any  proportions ;  but 
if  they  are  made  up  of  definite  particles,  then  in  any 
case  of  combination  one  or  two  or  more  of  these 
particles  must  combine  with  one  or  two  or  more  of  the 
similar  particles  of  another  gas  to  form  a  single  particle 
of  the  new  gas  which  is  being  made  from  them. 

Diffusion  of  Gases. — The  molecular  theory  is  also 
greatly  strengthened  by  the  rapidity  with  which  gases 
mix  when  in  contact  with  each  other.  Thus  a  little 
ammonia  is  spilled  in  one  part  of  the  room,  and  in  a 
very  short  time  its  presence  can  be  detected  by  its  odor 
in  all  parts  of  the  room.  If  a  paper  be  dipped  in 
hydrochloric  acid  and  brought  near  the  ammonia,  the 
white  fumes  of  ammonium  chloride  will  show  the  pres- 
ence of  both  gases  in  the  air.  This  flowing  of  one  gas 
into  another  is  called  Diffusion. 

Diffusion  of  Gases  through  a  Porous  Partition. 

LABORATORY  EXERCISE  29. — A  small  porous  cup,  such  as 
is  used  in  many  galvanic^  cells,  should  be  fitted  air-tight  with 
a  stopper  through  which  is  passed  a  glass  tube  of  one  or  two* 
millimeters  bore  and  about  thirty  centimeters  long.  Pre- 
pare a  hydrogen  generator  by  fitting  a  flask  with  a  tight 
cork  through  which  pass  two  glass  tubes.  One,  a  short  tube 
of  four  or  five  millimeters  in  diameter,  should  merely  enter 
the  neck  of  the  flask  and  should  project  on  the  outside  of 
the  cork  for  the  attachment  of  a  rubber  delivery-tube,  while 
the  other,  a  funnel  tube,  should  reach  nearly  to  the  bottom 
of  the  flask.  Put  some  scraps  of  commercial  zinc  which  has 
not  been  amalgamated  with  mercury  into  the  flask,  cover 
them  with  water,  and  pour  through  the  funnel  tube  enough 
sulphuric  acid  to  cause  a  brisk  chemical  action.  Invert  a 
beaker  or  other  vessel  slightly  larger  than  the  porous  cup 
over  the  top  of  the  delivery  tube,  and  allow  the  inverted 


PROPERTIES  OF  BODIES 


89 


vessel  to  be  filled  with  hydrogen.  Pass  the  porous  cup  up 
under  and  into  the  vessel  of  hydrogen,  letting  the  end  of  its 
tube  dip  in  a  vessel  of  water  meanwhile. 


FIG.  29. 

What  evidence  have  you  that  the  hydrogen  enters  the 
porous  cup  ? 

Remove  the  vessel  of  hydrogen  from  the  porous  cup. 
What  evidence  have  you  that  hydrogen  is  escaping  from  it  ? 
What  evidence  that  air  is  entering  ? 

Experiments  have  shown  that  if  the  glass  tube  had  been 
hermetically  sealed  the  hydrogen  would  have  entered  the 
cup  until  its  pressure  upon  the  inside  of  the  cup  was  as  great 
as  upon  the  outside.  Then  as  many  hydrogen  molecules 
would  pass  out  through  the  porous  walls  in  a  given  time  as 
\vould  enter  through  them  in  the  same  time,  and  the  pres- 
sures would  remain  constant, 


90  PHYSICS 

It  is  known  that  air  passes  in  and  out  through  the  porous 
walls  in  this  way  all  the  time,  but  when  the  cup  was  in 
hydrogen  gas,  the  hydrogen  entered  faster  than  the  air  passed 
out.  When  it  was  removed  the  hydrogen  escaped  faster  than 
the  air  entered.  What  proof  had  you  that  the  air  finally 
entered  ? 

What  reason  have  you  for  believing  that  the  molecules  of 
gases  are  in  rapid  motion  ? 

Do  the  molecules  of  air  or  of  hydrogen  apparently  move 
with  the  greater  velocities  ? 

Avogadro's  Theory. — We  have  seen  reasons  for 
believing  that  all  gases  are  very  similar  in  their  physical 
structure,  and  that  all  are  made  up  of  molecules  which 
are  constantly  in  motion,  and  which  move  with  differ- 
ent velocities  in  different  gases.  Avogadro,  an  Italian 
physicist,  in  1811,  and  Ampere,  a  French  physicist,  in 
1814,  arrived  independently  at  the  same  theory  to 
account  for  the  similarity  of  the  properties  of  different 
gases.  They  reasoned  that  if  one  gas  were  made  up 
of  large  molecules  far  apart  and  another  gas  of  small 
molecules  close  together,  the  laws  of  volume  change  for 
a  change  of  pressure  and  temperature  would  not  be  the 
same  in  the  two  gases ;  hence  that  in  equal  volumes  of 
gases  which  exert  the  same  pressure  at  the  same  tem- 
perature there  must  be  the  same  number  of  molecules 
at  the  same  average  distance  apart.  This  is  known  as 
Avogadro 's  Law,  and  it  is  the  assumption  upon  which 
the  modern  atomic  theory  in  chemistry  is  based.  It 
is  generally  stated,  "  Equal  volumes  of all  gases,  meas- 
ured tinder  standard  conditions  of  pressure  and  tem- 
perature, contain  the  same  number  of  molecules. ' ' 

This  law  can,  of  course,  never  be  experimentally 
proved.  The  gas  molecule  is  much  too  small  to  be 
seen  with  the  most  powerful  microscope,  even  if  it 
would  remain  at  rest  long  enough  to  be  observed,  and 


PROPERTIES  OF  BODIES  91 

we  have  seen  reasons  for  believing  that  it  is  always  in 
rapid  motion.  fc 

Cause  of  Gaseous  Pressure. — If,  as  we  believe,  the 
molecules  of  gases  are  very  numerous  and  in  constant 
motion,  they  must  frequently  collide  with  each  other 
and  with  the  walls  of  the  containing  vessel.  From  the 
third  law  of  motion,  we  know  that  the  momentum  of 
two  colliding  molecules  must  be  the  same  after  each 
impact  as  before,  and  if  they  are  perfectly  elastic,  so 
that  they  rebound  with  a  velocity,  equal  to  the  velocity 
of  impact,  as  do  the  ivory  balls  in  Exercise  18,  their 
collisions  will  never  bring  them  to  rest.  We  have  seen, 
too,  that  if  an  elastic  particle  strikes  the  wall  of  the 
containing  vessel  and  rebounds  with  a  velocity  equal 
to  its  velocity  of  impact,  its  momentum  before  striking 
is  mv  toward  the  enclosing  wall,  its  momentum  after 
rebound  is  mv  away  from  the  enclosing  wall,  or  —  mv\ 
hence  it  must  have  given  to  the  wall  a  momentum  2mv 
in  the  direction  of  its  motion  before  impact.  This 
momentum  would  act  as  a  pressure  upon  the  enclosing 
wall. 

Thus  suppose  a  gas  enclosed  in  a  tube  and  supporting 
a  column  of  mercury  resting  upon  it.  The  mercury, 
on  account  of  its  weight,  tends  to  fall  to  the  bottom  of 
the  tube,  but  it  is  supported  by  the  impacts,  of  the  gas 
molecules  upon  its  lower  side.  Many  millions  of  these 
molecules  are  supposed  to  impinge  upon  every  square 
millimeter  of  the  lower  surface  of  the  mercury  every 
second,  and  each  impact  gives  the  mercury  an  upward 
momentum  of  2niv,  where  m  is  the  mass  of  the  imping- 
ing molecule  and  v  its  velocity.  When  a  mercury 
column  in  a  horizontal  tube  separates  an  enclosed  gas 
volume  from  the  outside  air,  the  mercury  column  will 


92  PHYSICS 

come  to  rest  in  the  position  where  it  receives  as  much 
momentum  in  one  direction  from  the  enclosed  gas 
molecules  as  it  does  in  the  opposite  direction  from  the 
outside  air  molecules. 

If  the  enclosed  gas  is  compressed  so  that  the  same 
number  of  molecules  occupy  a  smaller  space,  more  of 
them  will  strike  the  wall  of  the  containing  vessel  in  a 
given  time,  and  will  accordingly  exert  a  greater  total 
pressure  upon  it.  Thus  if  the  air  column  in  the  Boyle's 
tube  be  compressed  to  half  its  original  volume,  the 
mercury  surface  will  be  struck  twice  as  often  by  the 
air  molecules.  For  suppose  a  cylindrical  tube  one 
meter  long  with  ends  of  some  elastic  substance,  as 
ivory,  and  suppose  an  ivory  ball  to  be  moving  length- 
wise of  the  tube  with  a  velocity  of  50  meters  a  second. 
It  will  move  the  length  of  the  tube  fifty  times  in  a 
second,  and  to  do  this  it  must  rebound  from  each  end 
twenty-five  times.  At  each  rebound  it  gives  to  the 
end  a  momentum  2mv,  and  in  each  second  a  momen- 
tum of  <,omv. 

Suppose  the  tube  to  be  shortened  to  one  half  its 
length  without  interfering  with  the  movement  of  the 
ball.  Evidently  each  end  of  the  tube  will  receive 
twice  as  many  impacts  as  before,  and  consequently 
twice  the  outward  momentum.  If  the  tube  contained 
a  million  ivory  balls,  the  conditions  would  be  practi- 
cally the  same;  for  while,  owing  to  the  collisions 
between  the  moving  balls,  the  impacts  upon  the  ends 
would  not  recur  at  regular  intervals,  still  the  same 
average  number  of  impacts  would  occur  in  any  con- 
siderable period  of  time.  If  instead  of  the  million  ivory 
balls  the  tube  contained  millions  of  millions  of  gas 
molecules  moving  with  velocities  of  some  hundreds  of 


PROPERTIES  OF  BODIES  93 

meters  a  second,  the  conditions  would  correspond  to 
what  we  believe  to  be  actually  taking  place  in  a  tube 
containing  an  enclosed  gas. 

We  suppose  a  gas,  then,  to  consist  of  a  very  large 
number  of  minute,  independent  bodies,  having  no 
action  upon  each  other  except  when  they  collide,  and 
acted  upon  by  no  force,  so  far  as  we  know,  except 
gravitation.  In  this  view,  the  molecules  of  gases  are 
as  much  independent  bodies  as  are  the  planets,  only 
they  are  confined  to  so  small  a  space  that  they  are  con- 
stantly colliding  with  each  other.  If  there  were  forces 
acting  between  them,  then  they  would  have  accelera- 
tions toward  or  from  each  other,  and  their  velocities 
would  change  with  the  distances  between  them. 

Thus,  suppose  a  quantity  of  gas  to  be  enclosed  in  a 
tube  provided  with  a  tight-fitting  piston,  and  let  the 
piston  be  suddenly  withdrawn  until  the  space  occu- 
pied by  the  gas  is  twice  as  great  as  before.  We 
know  that  the  gas  will  expand  suddenly  and  fill 
the  entire  space.  Suppose  a  repulsion  to  exist  be- 
tween the  gas  molecules  while  the  gas  is  expanding. 
This  repulsion  will  produce  accelerations  in  all  the 
molecules,  and  when  the  gas  has  occupied  the  larger 
volume  the  molecules  will  each  have  a  greater  veloc- 
ity and  a  greater  momentum  than  before.  Then, 
while  the  molecules  will  have  twice  the  distance  to 
travel  between  collisions  that  they  did  in  the  smaller 
volume,  they  will  travel  this  distance  in  less  than 
twice  the  time  and  will  accordingly  strike  upon  the 
piston  more  than  half  as  often  as  before,  while  at 
each  impact  they  will  give  it  a  greater  momentum 
than  formerly.  We  see,  then,  that  if  the  molecules  of 
a  gas  repel  each  other,  the  pressure  of  the  gas  will  not 


94  PHYSICS 

decrease  as  fast  as  its  volume  increases.  On  the  other 
hand,  if  the  molecules  attract  each  other,  their  veloci- 
ties will  be  less  when  the  gas  has  expanded  to  twice  its 
volume,  and  the  pressure  will  decrease  faster  than  the 
volume  increases. 

Pressure  Within  a  Gas  Equal  in  All  Directions. — 
This  theory  of  the  cause  of  gaseous  pressure  enables 
us  to  understand  how  the  pressure  at  any  point  within 
a  gas  is  equal  in  all  directions,  for,  on  the  average,  as 
many  molecules  are  moving  in  one  direction  as  in 
another.  This  is  not  true  when  currents  are  set 
up  in  the  gas,  as  in  that  case  the  molecules  have  a 
greater  average  momentum  in  one  direction  than  in 
any  other. 

Buoyant  Force  of  a  Gas. — It  is  a  familiar  fact  that 
Bodies  lighter  than  the  air  are  forced  upward  by  the 
pressure  of  the  air  molecules  under  them.  Thus  a 
balloon  filled  with  hydrogen  will  often  rise  to  a  great 
height.  In  this  case,  while  the  gas  within  the  balloon 
exerts  the  same  average  pressure  upon  its  walls  as  does 
the  outside  air,  its  downward  pressure  due  to  gravita- 
tion is  less  than  that  of  an  equal  volume  of  the  air. 
As  long  as  this  is  the  case,  the  air  under  the  balloon 
will  be  under  a  less  pressure  than  the  surrounding  air 
at  the  same  level.  This  means  that  fewer  molecules 
will  be  required  to  support  the  balloon  than  to  support 
the  downward  pressure  of  the  surrounding  air.  But  as 
fast  as  the  air  expands  and  decreases  its  density  under 
the  balloon  the  surrounding  molecules  diffuse  into  this 
region  and  equalize  the  density.  The  result  is  that  the 
balloon  is  pressed  upward  until  it  reaches  an  altitude 
where  the  density  of  the  air  is  no  greater  than  the 
density  of  the  balloon  and  its  enclosed  gas. 


PROPERTIES  OF  BODIES  95 

Molecular  Weights. 

The  density  of  oxygen  gas  is  sixteen  times  that  of 
hydrogen  gas.  If  Avogadro's  hypothesis  be  true,  what  is 
the  weight  of  an  oxygen  molecule  compared  with  that  of  a 
hydrogen  molecule  ? 

The  hydrogen  molecule  is  supposed  to  contain  2  atoms, 
and  the  weight  of  the  hydrogen  atom  is  taken  as  the  unit  of 
molecular  weights.  The  molecular  weight  of  hydrogen  is 
accordingly  2 ;  what  is  the  molecular  weight  of  oxygen  ? 

Carbon  dioxide  gas  has  twenty-two  times  the  density  of 
hydrogen ;  what  is  its  molecular  weight  ? 

Molecular  Velocities  and  Pressure. — In  our  consid- 
eration of  the  ivory  ball  moving  in  the  tube,  we  saw 
that  if  the  length  of  the  tube  were  shortened  one  half, 
the  pressure  upon  the  ends  due  to  the  impact  of  the 
ball  was  doubled.  Suppose  that  instead  of  shortening 
the  tube  one  half  the  velocity  of  the  ball  had  been 
doubled.  This  would  cause  twice  as  many  collisions 
with  the  ends  of  the  tube  as  before,  and  each  impact 
would  give  to  the  end  of  the  tube  twice  as  much 
momentum  as  before,  hence  the  total  pressure  upon  the 
ends  of  the  tube  would  be  four  times  as  great  as  before. 
If  the  velocity  of  the  ball  were  trebled,  its  pressure 
would  be  nine  times  as  great  as  before. 

The  pressure  would  increase  as  the  square  of  the 
velocity.  Hence  the  pressure  of  a  gas  upon  the  walls 
of  the  enclosing  vessel  must  vary  as  the  square  of  its 
average  molecular  velocity. 

The  kinetic  energy  of  a  moving  molecule  must  also 
vary  as  the  square  of  its  velocity.  The  average  kinetic 
energy  of  all  the  molecules  in  a  quantity  of  gas  will 
accordingly  vary  as  the  square  of  their  average  velocity 
varies.  Hence  the  pressure  of  a  gas  upon  the  walls  of 
the  enclosing  vessel  must  vary  as  the  average  kinetic 
energy  of  its  molecules  varies. 


96  PHYSICS 

Thus  since  the  oxygen  molecule  is  sixteen  times  as 
heavy  as  the  hydrogen  molecule,  it  must  have  sixteen 
times  the  momentum  at  the  same  velocity,  and  in  equal 
volumes  of  hydrogen  and  oxygen  if  the  molecules  move 
with  the  same  velocity,  the  oxygen  will  exert  sixteen 
times  the  pressure  of  the  hydrogen.  When  they  exert 
the  same  pressure,  the  hydrogen  molecules  must  have 
a  velocity  four  times  as  great  as  the  oxygen  molecules. 
This  makes  their  momentum  at  each  impact  one  fourth 
that  of  the  oxygen  molecules,  but  gives  them  four 
times  as  many  impacts  in  a  unit  of  time,  so  that  the 
total  momentum  given  to  the  enclosing  walls  is  the 
same  in  both.  It  also  makes  the  average  kinetic 
energy  of  the  oxygen  and  hydrogen  molecules  the 
same. 

The  Kinetic  Gas  Theory. — The  theory  by  which  the 
pressure  of  a  gas  is  explained  by  the  momentum  of  its 
molecules  is  known  as  the  Kinetic  Gas  Theory. 

LIQUID   STATE 

PROPERTIES   OF   LIQUIDS 

Cohesion.- — We  have  seen  that  Boyle's  Law  and  the 
laws  of  chemical  combination  can  be  explained  on  the 
hypothesis  that  a  gas  is  merely  an  aggregation  of 
independent  elastic  molecules  in  rapid  motion,  and  that 
these  molecules  can  only  be  held  together  in  a  mass 
by  an  external  pressure  applied  to  them,  and  that  they 
are  only  held  to  the  earth  by  the  gravitation  pressure. 
When  gases  are  under  very  great  pressures  Boyle's  Law 
does  not  apply  to  them.  At  a  pressure  which  is  differ- 
ent for  different  gases,  and  which  varies  with  the  tem- 
perature for  the  same  gas,  the  volume  of  the  gas  begins 


PROPERTIES  OF  BODIES  97 

to  decrease  faster  than  the  pressure  increases,  so  that 
the  product  pv  becomes  smaller  and  smaller.  This 
seems  to  indicate  that  when  the  molecules  are  brought 
close  together  there  is  an  attraction  between  them,  and 
that  when  they  are  held  so  close  together  that  they  do 
not  get  outside  the  range  of  this  attraction  a  smaller 
pressure  is  necessary  to  confine  them  to  this  volume 
than  would  be  necessary  if  the  attraction  did  not  exist. 
The  name  given  to  this  attraction  is  Cohesion.  If  the 
volume  be  sufficiently  diminished,  this  cohesion  attrac- 
tion increases  enormously  and  a  part  of  the  gas  changes 
into  the  liquid  form.  All  gases  may  be  changed  into 
liquids  in  this  way  if  only  the  temperature  be  not  too 
high. 

Vapor  Pressure  of  a  Liquid. — When  a  substance 
has  become  part  liquid  and  part  gas,  any  increase  of 
pressure  drives  some  of  the  gas  into  the  liquid  state, 
and  any  decrease  of  pressure  allows  some  of  the  liquid 
to  change  into  the  gaseous  state.  An  external  pressure 
is  a  necessary  condition  of  the  liquid  state.  In  some 
liquids,  as  in  mercury,  this  external  pressure  may  be 
very  small.  In  other  liquids,  as  ether  or  gasoline,  it 
becomes  very  considerable.  It  is  accordingly  impossi- 
ble to  maintain  a  perfect  vacuum  above  a  liquid. 

Measurement  of  Vapor  Pressure  of  a  Liquid. 

LABORATORY  EXERCISE  30. — The  gas  pressure  which  is 
necessary  to  permanently  maintain  the  liquid  state  of  aggre- 
gation is  called  the  vapor  pressure  of  the  liquid.  To 
measure  it,  proceed  as  follows: 

Fill  a  Torricellian  tube  about  a  centimeter  in  diameter 
with  mercury,  invert  it  in  the  mercury  cistern,  hold  it 
upright  by  means  of  a  support  and  clamp,  and  measure  the 
height  of  the  mercury  column.  By  means  of  a  pen-filler  or 
a  bent  glass  tube  pass  a  few  drops  of  water  into  the  bottom 


98  PHYSICS 

of  the  tube  under  the  mercury,  taking  care  that  no  air 
bubbles  enter.  The  water  will  rise  to  the  top  of  the  tube, 
and  some  of  it  will  at  once  change  into  the  gaseous  state. 
The  pressure  of  this  gas  causes  a  depression  of  the  mercury 
column.  What  is  the  vapor  pressure  of  water  in  centimeters 
of  mercury  from  your  experiment  ?  What  in  dynes  per 
square  centimeter  ? 

Refill  the  tube  with  mercury  and  repeat  the  experiment 
with  gasoline.  Lower  your  tube  in  the  cistern,  making  the 
space  above  the  mercury  as  small  as  possible.  Make  it  as 
large  as  possible.  Is  the  pressure  the  same  in  both  cases  ? 
Give  the  vapor  pressure  of  gasoline  at  the  temperature  of 
your  experiment. 

Comparison  of  Liquid  and  Gaseous  Properties. — 

We  have  seen  that  liquids  differ  from  gases  in  that  their 
molecules  no  longer  act  like  independent  bodies,  but 
are  held  together  by  an  attraction  or  pressure  called 
cohesion.  No  one  has  as  yet  been  able  to  explain  the 
cohesion  pressure  any  more  than  the  gravitation  pres- 
sure. We  only  know  that,  while  in  some  respects 
cohesion  and  gravitation  are  alike,  they  are  not  the 
same. 

In  their  physical  properties,  liquids  resemble  gases 
in  many  particulars.  Like  gases  they  have  very  little 
elasticity  of  form,  not  enough  to  support  any  consider- 
able pressure,  and  under  the  pressure  of  their  own 
weight  they  accordingly  take  the  shape  of  the  contain- 
ing vessel.  Unlike  gases,  they  offer  very  great  resist- 
ance to  compression,  and  it  is  believed  that  their 
molecules  are  so  close  together  that  they  have  very 
little  opportunity  for  free  motion.  That  they  are  still 
in  rapid  vibration  we  know  from  the  fact  that  some  of 
them  are  being  continually  bumped  off  from  the  surface 
with  a  sufficient  velocity  to  carry  them  outside  the 
range  of  cohesion  attraction.  It  is  only  when  the 


PROPERTIES  Of   BODIES  99 

molecules  confined  in  the  space  above  the  liquid 
become  so  numerous  that  as  many  of  them  strike  the 
liquid  surface  and  enter  it  as  are  sent  off  from  it  in  the 
same  time  that  a  constant  volume  of  the  liquid  is 
maintained. 

Elasticity  of  Form  in  Liquids. — That  liquids  do 
have  some  elasticity  of  form  is  shown  from  the  follow- 
ing considerations:  Small  drops  of  mercury  on  a  table 
or  on  an  iron  or  glass  plate  take  the  spherical  form. 
Falling  rain  drops  are  spherical.  In  the  manufacture 
of  shot,  the  molten  lead  is  allowed  to  fall  in  small 
drops  which  take  the  spherical  form  and  cool  while 
falling.  The  molten  beads  on  the  end  of  a  stick  of 
sealing-wax  or  a  glass  rod  take  the  spherical  form. 
We  accordingly  infer  that  larger  masses  of  liquid,  if 
freed  from  the  gravitation  pressure,  would  take  the 
spherical  form. 

Form  of  a  Liquid  Removed  from  Gravitation. 

LABORATORY  EXERCISE  31. — Pour  a  little  water  into  a  glass 
vessel  (one  with  flat  sides,  as  a  flat-sided  bottle,  preferred), 
and  on  this  water  pour  enough  salad  oil  or  other  oil  to  form 
a  mass  about  a  centimeter  in  diameter.  Then  pour  through 
a  tube  which  reaches  to  the  bottom  of  the  water  about  one 
and  a  half  times  its  volume  of  commercial  (95  per  cent) 
alcohol.  This  will  mix  gradually  with  the  water  and  will 
form  a  liquid  of  about  the  same  density  as  the  oil.  If  too 
much  alcohol  be  added,  the  oil  globule  will  sink  to  the 
bottom,  and  can  be  made  to  rise  in  the  liquid  by  adding  a 
little  water.  If  the  oil  rises  to  the  top,  add  more  alcohol, 
putting  it  in  as  near  the  bottom  of  the  water  as  possible  so 
that  it  may  mix  rapidly.  A  very  few  trials  will  enable  you 
to  prepare  a  solution  in  which  the  oil  will  float  entirely 
submerged,  as  shown  in  Fig.  30. 

What  is  the  shape  of  the  submerged  oil  globule  ?  (Note 
that  if  you  are  looking  through  the  curved  sides  of  a 
cylindrical  vessel  the  shape  of  the  globule  is  distorted.) 


100 


PHYSICS 


Press  it  out  of  shape  with  a  glass  tube,  and  note  the  rate  at 
which  it  returns  to  its  original  shape.  Has  it  any  elasticity 
of  form  ?  Has  it  enough  to  support  its  own  weight  ?  What 
reason  have  you  for  thinking  that  it  is  pressed  upon  equally 
on  all  sides  by  the  surrounding  liquid  ? 

Note  the  appearance  as  if  of  a  liquid  skin  over  the  surface 
of  the  oil,  so  that  it  acts  like  a  rubber  membrane  filled  with 


FIG.  30. 

a  fluid.     If  the  oil  were  held  together  by  the  contraction  of 
an  elastic  membrane,  what  shape  would  it  take  ? 

Contraction  of  Surface  Film  of  Liquids. — Very 
many  examples  of  the  contraction  of  the  surface  film  of 
water  are  familiar  to  every  one.  The  hairs  of  your 
head  cling  together  when  wet,  held  by  the  water 
between  them.  Water  may  be  carried  in  a  sieve  whose 
wires  have  been  coated  with  paraffin  so  that  the  water 
will  not  cling  to  them,  the  weight  of  the  water  in  the 
meshes  of  the  sieve  being  supported  by  the  strength  of 
the  surface  film.  An  oiled  needle  may  be  floated  upon 
water,  held  up  by  the  surface  film. 

Experiments  with  Surface  Films. 

LABORATORY  EXERCISE  32. — Perform  some  or  all  of  the 
following  experiments  on  the  contraction  of  the  surface 
film. 


PROPERTIES  OF  BODIES 


101 


Blow  a  small  soap  bubble,  and  note  its  change  in  size 
while  holding  the  pipe  with  the  stem 
open  to  the  air.  Hold  the  end  of 
the  stem  near  a  lighted  candle  and 
see  if  an  air  current  is  entering  or 
leaving  it. 

Make  a  ring  of  wire  about  three 
or  four  inches  in  diameter  and  tie 
a  loop  of  thread  in  it  as  shown  in 
Fig.  31.  Dip  the  ring  into  a  soap 
solution  and  lift  it  out  with  a  soap 
film  clinging  across  it.  The  thread 
loop  will  then  float  about  in  the 
film.  Break  the  film  inside  the  loop 
by  touching  it  with  a  hot  wire,  and 
explain  what  occurs. 

Dip  a  funnel  in  a  soap  solution 
and  take  it  out  with  a  soap  film 
across  its  mouth.  Hold  the  funnel 
with  the  stem  open  and  explain  the 
movement  of  the  film. 

Pour  enough  water  into  a  plate 
or  flat  -  bottomed  vessel  to  just 
cover  the  bottom  with  a  thin  layer. 
Pour  a  drop  of  alcohol  upon  this 
water.  Does  the  alcohol  increase 
or  diminish  the  surface  contraction  of  water  ? 

Float  a  piece  of  paper  on  water  and  with  a  glass  tube 
touch  a  drop  of  alcohol  to  one  edge  of  the  paper.  Explain 
the  movement  of  the  paper. 

Hold  a  small  glass  tube  vertical  in  water  and  note  the 
height  at  which  the  water  stands  in  the  tube.  What  sup- 
ports the  weight  of  the  water  column  ? 

Fill  a  dry  tumbler  heaping  full  of  water  and  then  drop 
small  stones  or  nails  into  the  water  as  long  as  possible  before 
the  water  overflows.  What  evidences  do  you  see  of  a  con- 
tracting surface  film  ?  ^^ 

Formation  of  Surface  Film  by  Cohesion. — All  of 

the  above  experiments  have  shown  an  apparent  con- 
traction of  the  surface  layer  of  water.      This  apparent 


FIG.  31. 


102  PHYSICS 

contraction  of  the  surface  film  may  be  explained  by  the 
action  of  cohesion. 

Thus,  suppose  a  molecule  within  the  body  of  a  liquid 
attracted  by  all  the  surrounding  molecules  within  the 
range  of  the  cohesion  attraction.  Since  these  molecules 
are  uniformly  distributed  about  it,  the  molecule  will 
have  no  tendency  to  move  in  one  direction  more  than 
another,  and  its  freedom  of  motion  will  in  no  way  be 
affected  by  any  molecules  except  those  that  may  be  in 
direct  contact  with  it.  With  a  molecule  on  the  surface 
of  the  liquid  the  case  is  different;  for  since  the  attracting 
molecules  are  all  below  it,  their  resultant  attraction  is 
downward.  This  may  also  be  true  of  the  resultant  attrac- 
tion for  molecules  at  small  distances  below  the  surface. 

Thus,  let  MN  in  Fig.  32  represent  the  trace  of  a 
liquid  surface  and  let  m  be  a  molecule  below  this  sur- 
face. Let  the  circle  about  m  as  a  center  represent  the 
circumference  of  the  sphere  of  molecular  attraction. 
That  is,  all  molecules  within  this  sphere  will  be  near 
enough  m  to  exert  an  attractive  force  upon  it,  while 
molecules  outside  of  this  sphere  will  have  no  influence 
whatever  upon  /#. 


FIG.  32. 

Let  M'N'  be  a  plane  parallel  to  MN  and  as  far 
below  m  as  MN  is  above  it.  Then  the  forces  exerted 
upon  ;;/  by  all  the  molecules  between  these  planes  will 


PROPERTIES  OF  BODIES 


103 


just  balance  each  other;  that  is,  there  will  be  always 
on  opposite  sides  of  m  the  same  number  of  molecules 
at  the  same  distances  from  m.  The  molecules  in  the 
part  of  the  sphere  below  M'N'  will,  however,  exert  an 
attraction  upon  m  which  will  not  be  balanced  by  any 
corresponding  attraction  upward,  since  the  correspond- 
ing part  of  the  other  hemisphere  lies  outside  the  liquid 
surface.  The  resultant  of  all  the  forces  on  m  will 
accordingly  be  a  downward  pressure  perpendicular  to 
the  liquid  surface.  This  will  be  true  for  any  molecule 
whose  distance  from  the  surface  is  less  than  the  radius 
of  the  sphere  of  molecular  attraction. 

Influence  of  Curvature  of  Surface  on  Surface  Ten- 
sion.— On  a  convex  surface  the  attraction  of  a  molecule 
below  the  surface  toward  the  surface  will  be  less  than 
on  a  plane  surface,  and  on  a  concave  surface  it  will  be 
greater.  Thus  it  will  be  seen  that  ml  has  fewer  mole- 
cules attracting  it  toward  the  surface  and  m2  a  greater 


FIG.  33- 

number- than  if  they  were  at  the  same  distance  below 
a  plane  surface.  The  pressure  of  the  surface  film  upon 
a  liquid  will  accordingly  be  greater  the  more  convex 
the  surface,  and  less  the  more  concave  the  surface. 

Surface  Tension  on  Soap  Bubble. — In  the  case  of  a 
soap  bubble,  which  is  bounded  by  two  films,  the  one 


io4  PHYSICS 

convex  and  the  other  concave,  the  pressure  upon  the 
convex  outer  surface  will  be  greater  than  upon  the 
concave  inner  surface,  and  the  resultant  of  the  two 
pressures  will  be  an  inward  pressure  upon  the  confined 
air.  In  the  oil  globule,  the  pressure  of  the  surface  film 
can  be  uniform  only  when  the  curvature  of  the  surface 
is  everywhere  the  same.  Thus  this  pressure  upon  the 
whole  free  surface  of  a  liquid  has  the  effect  of  a  con- 
tracting membrane  which  continually  exerts  a  pressure 
upon  the  enclosed  liquid. 

V  Pressure  of  Surface  Tension  on  Opposite  Sides  of  a 
Soap  Film. 

LABORATORY  EXERCISE  33. — In  the  case  of  a  soap  film  on 
a  wire  frame,  the  pressure  upon  the  air  can  never  be  greater 


FIG.  34. 

on  one  side  than  on  the  other,  since  the  atmospheric  pres- 
sure is  the  same  in  all  directions.  Consequently,  when  the 
film  is  made  convex  in  one  direction,  it  becomes  concave  in 
a  direction  at  right  angles  to  the  convexity,  and  thus  the 
increased  pressure  on  the  convex  surface  is  balanced  by  a 
decreased  pressure  over  the  concave  surface. 

Make  a  rectangular  wire  frame,  dip  it  into  a  soap  solution 


PROPERTIES  OF  BODIES  105 

and  take  it  out  with  a  film  across  it.  Bend  the  frame  so 
that  the  film  becomes  convex  on  one  side,  as  in  Fig.  34,  and 
note  how  the  increased  pressure  of  this  convex  film  is  bal- 
anced by  the  corresponding  convexity  at  right  angles  to  it  of 
the  film  on  the  other  surface.  Observe  the  equality  of  the 
two  curvatures  at  right  angles  to  each  other. 

Measurement  of  Surface  Tension.  —  The  force 
exerted  by  a  strip  of  unit  width  of  the  surface  film  of  a 
liquid  is  called  the  Surface  Tension  of  the  liquid.  The 
tables  of  surface  tension  of  liquids  generally  give  the 
weight  in  milligrams  which  can  be  supported  by  a  strip 
of  the  surface  film  one  millimeter  wide. 

Thus  if  a  wire  be  bent  in  the  shape  A  BCD  and  a 


c 


FIG.  35. 

straight  wire  or  straw  ab  be  laid  across  it  and  a  soap 
film  be  spread  over  the  rectangle  thus  formed,  the  con- 
traction of  this  film  will  pull  ab  toward  BC.  To 


106  PHYSICS 

prevent  this  a  weight  can  be  attached  to  ab  which  will 
just  balance  the  contraction.  If  the  number  of  milli- 
grams of  weight  required  be  divided  by  the  number  of 
millimeters  between  AB  and  CD,  it  will  give  the  con- 
tractile force  of  the  film  in  milligrams  per  millimeter  in 
width  of  the  film.  But  this  contractile  force  is  due  to 
two  surface  films,  one  on  each  side  of  the  soap  film, 
hence  the  half  of  the  force  found  will  represent  the 
surface  tension  of  a  soap  solution. 

Surface  Tension  in  Capillary  Tubes. — One  of  the 
best  known  methods  of  measuring  surface  tension  is  by 
the  height  of  the  column  supported  in  small  glass  tubes 
called  Capillary  (hair-like)  Tubes.  Because  capillary 
tubes  have  been  used  so  much  in  measuring  surface 
tension,  the  name  Capillarity  has  sometimes  been  given 
to  surface  tension,  and  the  measure  of  the  surface  ten- 
sion of  a  given  liquid  is  often  called  its  Capillary 
Constant. 

Measurements  of  Capillary  Constants. 

LABORATORY  EXERCISE  34. — Select  a  clean  glass  tube  of 
small  bore  and  measure  the  diameter  of  the  bore  as  accurately 
as  you  can  by  means  of  the  vernier  calipers.  Place  the  tube 
vertical  in  a  vessel  of  clean  water.  Raise  and  lower  the 
tube,  and  observe  whether  the  water  column  in  it  stands 
always  at  the  same  height  above  the  water  in  the  vessel.  If 
it  does  not,  the  tube  is  not  clean  or  is  not  of  uniform  bore. 

Note  that  when  the  tube  is  raised,  the  part  that  is  pulled 
out  of  the  water  remains  wet,  hence  is  covered  by  a  surface 
film  of  water;  consequently  this  surface  film  must  stretch 
when  the  tube  is  raised  and  contract  when  it  is  lowered. 
Since  the  contracting  film  surrounds  the  inside  of  the  tube, 
its  width,  if  it  could  be  straightened  out  to  a  plane  surface, 
would  be  the  inner  circumference  of  the  tube.  This  inner 
circumference  is  27zr,  where  r  is  the  radius  of  its  bore. 
Calculate  the  width  of  the  film  for  your  tube. 

The  force  which  stretches  the  film  is  the  weight  of  the 
water  column  which  it  supports.  The  weight  of  this  column 


PROPERTIES  OF  BODIES  107 

in  grams  is  its  volume  in  cubic  centimeters  times  its  density, 
or,  in  milligrams,  its  volume  in  cubic  millimeters  times  its 
density.  Its  volume  is  found  by  multiplying  its  cross-sec- 
tion by  its  height.  Its  cross-section  is  Tzr2.  Its  volume  is 
itr*h,  and  its  weight  is  nr^hd.  Hence  the  surface  tension  is 
_  nr*hd  __  hrd 
2  ' 


Calling  the  density  of  water  i,  what  is  its  surface  tension 
from  your  measurements  ? 

Calling  the  density  of  alcohol  .8,  measure  its  Capillary 
Constant. 

Assuming  the  density  of  a  soap  solution  to  be  the  same 
as  that  of  pure  water,  is  its  capillary  constant  greater  or  less 
than  that  of  water  ? 

If  the  surface  tension  of  chloroform  is  2.  73  and  its  density 
1.48,  how  high  will  the  liquid  stand  in  a  tube  of  i  millimeter 
diameter  ? 

Olive  oil  of  density  .9  stands  14.4  millimeters  high  in  a 
tube  of  i  millimeter  diameter.  What  is  its  surface  tension  ? 

Our  equation  for  surface  tension  is  T=  —  .     This  may 

2T  2T 

be  written  —  =  hr.     Since  for  a  given  liquid  —  is  a  con- 

stant, we  can  write  hr  =  a  constant,  or  h  varies  inversely 
as  r.  Hence  in  any  given  liquid  the  heights  of  the  capillary 
columns  in  different  tubes  are  inversely  as  the  radii  of  the 
tubes. 

Pure  water  in  a  clean  tube  i  millimeter  in  diameter  will 
stand  about  29  millimeters  high.  What  is  the  diameter  of 
the  tube  in  which  it  stands  only  7  millimeters  high  ? 

Surface  Tension  of  Mercury.  —  Mercury  will  not  rise 
in  a  glass  tube  because  its  surface  tension  is  greater 
than  its  attraction  for  the  glass.  It  accordingly  stands 
lower  in  a  glass  tube  than  outside,  and  the  top  of  the 
column  in  the  tube,  called  the  meniscus,  is  convex  in 
mercury  instead  of  concave  as  in  water.  Mercury 
drops  are  much  heavier  than  water  drops  and  yet 
maintain  their  spherical  form  much  better,  hence  we 


io8     ^  PHYSICS 

know  that  the  surface  tension  of  mercury  is  much 
greater  than  that  of  water.  In  fact,  measurements  by 
other  methods  have  given  the  surface  tension  of  mer- 
cury as  55,  while  the  same  methods  gave  for  water  only 
8.25.  Mercury  clings  to  many  metals  as  water  does 
to  glass,  and  in  tubes  of  these  metals  the  surface  ten- 
sion of  mercury  could  be  calculated  from  its  capillary 
height. 

If  Tis  55  and  d  13.6,  what  would  be  the  value  of  h  in  a 
i  millimeter  capillary  tube  to  which  mercury  would  adhere  ? 

Magnitude  of  Cohesion. — It  is  impossible  to  measure 
the  cohesion  attraction  between  two  liquid  surfaces  at 
molecular  distances  from  each  other,  since  we  do  not 
know  how  great  the  molecular  distances  are  nor  at 
what  rate  the  attraction  falls  off  with  the  distance. 
We  know,  however,  from  the  work  required  to  separate 
two  such  surfaces  that  the  cohesion  pressure  between 
them  is  very  great.  Thus,  if  two  glass  plates  having 
plane  faces  I  centimeter  square  have  a  water  film 
between  them  and  are  pulled  apart,  it  requires  the 
expenditure  of  147  ergs  of  energy  to  separate  them. 
If  they  could  be  kept  absolutely  parallel  to  each  other, 
so  that  the  two  layers  of  water  on  the  plates  would  be 
everywhere  equally  distant  from  each  other,  then  147 
ergs  of  work  would  be  done  in  moving  one  water  sur- 
face against  the  force  of  cohesion  to  the  distance  at 
which  cohesion  ceases  to  act.  This  distance  has  been 
experimentally  determined,  and  while  the  accuracy  of 
the  determination  is  not  great,  still  the  distance  may 
be  taken  as  about  six  millionths  of  a  centimeter.  If 
cohesion  were  a  constant  force  acting  through  this  dis- 
tance, we  could  compute  its  value  from  the  equation 


PROPERTIES  OF  BODIES  109 

F=  ~S  =  .000006  =  24>  500,ooo  dynes,  or  the  weight 
of  about  25,000  grams. 

Since,  however,  the  force  is  zero  at  a  distance  of  six 
millionths  of  a  centimeter  and  increases  to  a  maximum 
at  the  least  distance  of  the  surfaces  from  each  other,  it 
must  be  thousands  of  times  this  much  at  this  least  dis- 
tance, so  that  it  is  probable  that  the  two  surfaces  when 
in  liquid  contact  are  held  together  by  a  pressure  of 
more  than  a  ton  to  the  square  centimeter.  Since  the 
cohesion  pressure  is  so  great  while  the  distance  through 
which  it  acts  is  so  small,  it  is  supposed  to  decrease  at 
a  higher  rate  than  gravitation  does.  The  higher  this 
rate,  the  greater  is  the  attraction  at  molecular  distance. 

Compressibility  of  Liquids. — From  the  magnitude 
of  cohesion,  we  should  expect  an  enormous  external 
pressure  to  be  required  to  measurably  compress  a  liquid 
volume.  In  fact,  the  earlier  attempts  at  the  compres- 
sion of  water  led  to  the  conclusion  that  water  was 
incompressible.  Later  experiments  have  shown  that 
all  liquids  are  slightly  compressible.  Thus  water  at 
o°  C.  has  its  volume  decreased  by  about  .00005  °f 
itself  for  a  pressure  of  one  atmosphere.  The  atmos- 
phere has  its  volume  decreased  one  half  by  this  pres- 
sure, hence  air  at  standard  pressure  is  about  ten 
thousand  times  as  compressible  as  water.  Ether  is 
nearly  three  times  as  compressible,  and  mercury  is 
about  one  sixteenth  as  compressible,  as  water. 

Viscosity. — It  is  a  common  observation  that  all 
liquids  do  not  flow  with  equal  freedom.  This  differ- 
ence is  very  marked  in  two  such  liquids  as  water  and 
molasses  or  honey.  In  fact,  some  liquids  have  con- 
siderable elasticity  of  form,  and  differ  from  solids  only 


no  PHYSICS 

in  that  this  elasticity  is  not  great  enough  to  support 
the  weight  of  the  body. 

The  resistance  which  one  liquid  surface  meets  with 
in  moving  over  another  liquid  surface  is  called  Vis- 
cosity. Its  cause  is  not  well  known.  If  the  molecules 
of  a  liquid  are  perfectly  spherical  in  shape,  they  can 
meet  with  little  resistance  in  rolling  over  each  other, 
even  if  they  are  in  actual  contact.  If  they  are  of  irreg- 
ular shapes,  then  they  may  move  over  each  other  with 
difficulty.  It  is  known  that  all  liquids  can  be  com- 
pressed into  smaller  space  under  a  sufficiently  heavy 
pressure,  hence  their  molecules  must  have  some  room 
for  motion. 

If  cohesion  is  not,  like  gravitation,  a  force  acting 
between  the  centers  of  gravity  of  the  molecules,  but, 
like  magnetism,  a  force  acting  between  definite  points 
on  the  surface  of  the  molecules,  then  the  molecules  will 
tend  to  cling  together  in  strings,  as  would  a  mass 
made  up  of  small  magnets,  and  this  would  hinder  the 
flow  of  the  liquid.  We  shall  see  later  that  there  is 
some  ground  for  believing  cohesion  to  act  in  this  way. 

The  peculiar  properties  of  many  liquid  films  depend 
upon  the  viscosity  of  the  liquid.  Thus  a  soap  film  has 
less  surface  tension  but  greater  viscosity  than  pure 
water.  If  a  soap  film  be  stretched  across  a  wire  frame 
and  supported  in  a  vertical  position,  the  liquid  will 
slowly  run  down  to  the  bottom,  and  the  soap  film  will 
grow  thinner  at  the  top.  When  it  becomes  too  thin  to 
support  the  weight  of  the  liquid  below,  it  will  break  at 
the  top.  The  more  viscosity  the  liquid  has,  the  longer 
will  the  film  stand  before  breaking.  For  the  same 
reason,  a  soap  bubble  left  standing  becomes  thin  at  the 
top  and  finally  breaks. 


PROPERTIES  OF  BODIES 


in 


In  liquids  having  small  surface  tension  and  great 
viscosity  air  bubbles  may  stand  for  a  long  time  without 
breaking.  Such  liquids  are  said  to  * '  froth  ' '  readily 
when  shaken  up  with  air. 

Diffusion  of  Liquids. 

LABORATORY  EXERCISE  35. — Provide  a  wide-mouthed  bottle 
or  a  deep  tumbler  with  a  siphon  which  reaches  to  within 
about  one  inch  of  the  bottom.  Fill  the  bottle  nearly  full  of 
clear  water  and  let  some  of  it  run  out 
through  the  siphon.  Close  the  siphon 
while  full  of  water  with  a  cork  or  a 
rubber  tube  and  pinch-cock.  Through 
a  glass  funnel-tube  reaching  to  the 
bottom  of  the  tumbler  pour  a  strong 
solution  of  copper  sulphate  until  it 
rises  just  above  the  end  of  the  siphon. 
Open  the  siphon  and  allow  the  liquid 
to  run  out  until  there  is  a  perfectly 
clear  plane  of  separation  between  the 
heavier  solution  and  the  lighter  water. 
Then  close  the  siphon  and  allow  the 
tumbler  to  stand  undisturbed  and  note 
the  rate  at  which  the  copper  sulphate 
diffuses  into  the  water  above  it.  How 
does  liquid  diffusion  compare  in  velocity  with  gaseous  dif- 
fusion ? 

Do  the  molecules  in  a  liquid  retain  their  positions,  or  do 
they  move  about  through  the  liquid  ? 

Influence  of  Viscosity  on  Diffusion. — The  rate  of 
diffusion  of  liquids  depends  greatly  upon  their  viscosity. 
If  a  strong  syrup  of  sugar  be  placed  in  the  tumbler 
instead  of  the  copper  sulphate,  it  will  diffuse  into  the 
water  much  more  slowly,  and  mucilage  or  glue  will 
diffuse  much  more  slowly  than  sugar. 

Diffusion  Through  Porous  Membrane. 

LABORATORY  EXERCISE  36. — Tie  a  piece  of  wet  parchment 
paper  tightly  over  the  opening  of  a  long-stemmed  funnel  or 
a  thistle  tube,  pour  a  strong  sugar  solution  into  the  funnel 


FlG 


112 


PHYSICS 


until  it  rises  into  the  stem,  and  suspend  it  in  clear  water  so 
that  the  liquid  will  be  at  the  same  height  inside  and  outside 
the  tube.  Leave  it  in  this  position,  and 
determine  if  diffusion  takes  place  through 
the  parchment  paper.  Is  the  rate  of 
diffusion  the  same  in  both  directions  ? 
Does  it  require  a  greater  pressure  to 
force  the  water  through  the  membrane 
into  the  solution,  or  out  of  it  ?  Is 
cohesion  apparently  greater  within  the 
solution  or  within  the  pure  water  ?  Do 
you  find  evidence  that  the  sugar  diffuses 
through  the  membrane  ? 

Osmosis. — The  first  observation 
on  the  diffusion  of  liquids  through  a 
porous  membrane  was  made  by  the 
Abbe  Nollet  in  1748.  He  observed 
the  different  rates  of  diffusion  of 
water  and  alcohol  through  an  ani- 
mal membrane,  using  a  pig's  bladder 
FIG.  37.  filled  with  alcohol  and  immersed  in 

water.     The  name  Osmose,  or  Osmosis,  has  been  given 
to  this  membrane  diffusion. 

Osmotic  Pressure. — In  the  Abbe  Nollet 's  experi- 
ment the  water  entered  through  the  walls  of  the  bladder 
faster  than  the  alcohol  escaped  and  the  bladder  became 
distended  by  a  great  pressure.  In  the  case  of  the  sugar 
solution  in  water,  if  the  solution  had  been  placed  in  a 
closed  vessel,  the  pressure  exerted  by  the  water  diffus- 
ing into  the  solution  would  have  broken  the  paper. 
The  pressure  of  the  enclosed  fluid  upon  the  walls  of  the 
containing  vessel  is  called  Osmotic  Pressure. 

From  the  importance  of  osmotic  action  in  physio- 
logical processes,  such  as  respiration,  secretion,  excre- 
tion, and  the  like,  and  from  the  fact  that  some  recent 


PROPERTIES  OF  BODIES  113 

physical  theories  attach  great  importance  to  it,  the 
phenomenon  of  osmotic  pressure  has  for  several  years 
attracted  much  attention.  It  has  been  found  possible 
to  prepare  partitions  which  will  allow  only  water  to 
diffuse  through  them.  This  is  done  by  precipitating 
some  insoluble  substance,  as  Baric  Sulphate  or  Copper 
Ferrocyanide,  within  the  walls  of  a  porous  cup.  By 
means  of  these  so-called  semi-permeable  cells  much 
greater  osmotic  pressures  can  be  observed  than  in 
cells  which  allow  both  substances  to  diffuse  through 
them. 

Thus  water  will  diffuse  into  a  one  per  cent  solution 
of  saltpeter  until  it  produces  an  osmotic  pressure  of 
more  than  three  atmospheres.  This  pressure,  while 
very  considerable,  is,  we  know,  very  small  as  compared 
with  the  total  cohesion  pressure. 

Evaporation. — It  has  already  been  observed  that  an 
external  pressure  is  necessary  for  the  maintenance  of 
the  liquid  state.  This  pressure  must  be  a  pressure  due 
to  the  vapor  of  the  liquid.  When  the  molecules  on 
the  surface  of  a  liquid  are  driven  off  by  the  impact  of 
molecules  below  them,  they  at  once  become  free  gas 
molecules,  and  if  they  escape  into  the  air  they  are 
knocked  about  by  the  air  molecules  and  are  not  likely 
ever  to  return  to  the  liquid  surface  again.  If  they 
escape  into  an  enclosed  space  above  the  liquid,  this 
space  finally  becomes  so  filled  with  them  that  as  many 
strike  the  liquid  surface  and  enter  through  it  as  escape 
from  it  in  the  same  time.  Then,  though  the  exchange 
of  molecules  between  the  liquid  and  its  vapor  is  con- 
stantly going  on,  the  total  quantities  of  liquid  and 
vapor  remain  the  same.  This  escape  of  molecules 
from  the  liquid  surface  is  called  evaporation.  It  goes 


PHYSICS 


on  at  all  temperatures,  but  much  more  rapidly  at  high 
temperatures  than  at  low. 

Evaporation  takes  place  on  a  large  scale  all  over  the 
surface  of  the  earth.  The  rain  which  falls  upon  the 
earth  has  all  been  raised  by  evaporation. 

If  a  basin  of  water  with  vertical  walls  be  exposed  to 
the  air  for  several  days,  the  depth  of  water  evaporated 
in  a  day  can  be  easily  measured. 

Boiling. — When  ordinary  water  is  poured  into  a  glass 
it  always  contains  many  small  air  bubbles.  These 
bubbles  usually  cling  to  the  sides  of  the  glass,  and 
when  expanded  by  heat  they  can  be  easily  seen. 
Evaporation  must  take  place  into  these  bubbles  as  into 
the  outside  air.  As  the  temperature  of  the  water  is 
raised,  its  vapor  pressure  in  the  air  bubbles  increases. 
As  long  as  this  pressure  is  less  than  the  pressure  of  the 
external  air  on  the  surface  of  the  water  the  bubbles  do 
not  expand  and  break  through  the  water  into  the  out- 
side air.  When  the  pressure  within  the  bubble  becomes 
greater  than  the  atmospheric  pressure,  the  bubbles 
expand  and  break  and  their  vapor 
escapes  into  the  air.  This  process 
is  called  boiling. 

Vapor  Pressure  of  a  Boiling  Liquid . 

LABORATORY  EXERCISE  37. — A  J-shaped 
tube  about  a  centimeter  in  diameter  with 
the  short  arm  closed  about  four  or  five 
centimeters  above  the  bend  has  the  short 
arm  and  the  bend  filled  with  gasoline  or 
some  other  volatile  liquid,  so  that  no 
air  remains  above  the  liquid  in  the  closed 
arm.  A  vessel  of  boiling  water  is  carried 
FIG.  38.  to  some  distance  from  a  flame,  and  the 

tube  of  gasoline  is  lowered  into  it.     The  gasoline  boils,  and 
while  some  of  its  vapor  escapes  through  the  open  arm  into  the 


PROPERTIES  OF  BODIES  115 

air  another  part  gathers  in  the  closed  arm.  How  can  you 
know  when  the  vapor  pressure  in  the  closed  arm  is  equal  to 
the  atmospheric  pressure  ?  How  does  the  vapor  pressure  of 
boiling  gasoline  compare  with  the  atmospheric  pressure  ? 

Condensation. — In  your  experiments  on  vapor  pres- 
sure you  saw  that  the  pressure  of  a  vapor  above  a  liquid 
is  independent  of  the  space  which  it  occupies.  It  must 
be,  then,  that  any  increase  of  pressure  drives  some  of 
the  molecules  into  the  liquid  state,  as  otherwise  the 
pressure  would  increase  when  the  volume  decreased. 
This  change  from  the  gaseous  to  the  liquid  state  is 
called  condensation.  It  may  be  effected  by  increasing 
the  pressure  on  a  vapor  or  by  lowering  its  temperature. 
It  will  be  considered  more  fully  under  the  subject  of 
Heat. 

MECHANICS  OF   FLUIDS 

Conditions  of  Equilibrium  in  Fluids. — We  have 
seen  that  a  pressure  applied  to  any  part  of  the  body  of 
a  gas  is  transmitted  very  soon  to  all  parts  of  the  gas. 
That  this  transmission  is  not  instantaneous  can  be  seen 
in  blowing  a  soap  bubble.  If  the  air  is  blown  in  under 
great  pressure,  the  bubble  may  become  elongated,  but 
it  assumes  the  spherical  form  almost  immediately  after 
the  pressure  is  removed.  It  would,  accordingly,  be 
impossible  for  a  confined  gas  to  maintain  a  greater 
pressure  on  one  part  of  its  surface  than  on  another, 
because  the  molecules,  being  free  to  move,  would  move 
into  the  region  of  least  pressure  until  the  pressure  was 
equalized.  The  only  exception  to  this  is  the  case  of 
the  gravitation  pressure.  A  gas  in  an  enclosed  vessel 
presses  downward  more  than  upward  by  an  amount 
equal  to  its  weight. 


n6  PHYSICS 

Since  the  molecules  of  a  liquid  are  also  free  to  move 
about,  they  will  likewise  move  toward  regions  of  least 
pressure  until  the  pressure  is  equalized.  Thus  all 
liquids  sooner  or  later  come  to  rest  with  their  upper 
surfaces  level,  so  that  the  gravitation  pressure,  the 
atmospheric  pressure,  and  the  surface  tension  are  all 
uniform  over  the  surface.  In  mobile  liquids,  like  water, 
this  position  of  equilibrium  is  soon  reached.  In  viscous 
liquids,  like  tar,  it  may  not  be  reached  for  a  long  time ; 
but  unless  the  liquid  has  sufficient  rigidity  to  resist 
permanently  an  external  pressure,  the  pressure  will 
finally  be  equalized  throughout  the  liquid.  One  condi- 
tion of  equilibrium  in  a  liquid  or  gas  is,  then,  that  the 
external  pressure  (not  counting  the  pressure  due  to  its 
own  weight)  must  be  everywhere  the  same  on  equal 
areas  of  its  surface. 

Water  or  any  other  mobile  liquid  will  accordingly 
stand  at  the  same  level  in  communicating  vessels  or 
tubes,  so  long  as  the  tubes  are  not  small  enough  for 
the  surface  tension  to  appreciably  raise  the  water  sur- 
face within  them. 

Transmission  of  Pressure. — Suppose  two  communi- 
cating cylinders  of  water,  one  having  a  cross-section  of 
I  square  centimeter,  and  the  other  having  a  cross- 
section  of  100  square  centimeters.  The  water  will 
stand  at  the  same  height  in  both  cylinders.  Suppose 
I  centimeter  in  depth  of  water  to  be  added  to  each 
cylinder.  The  water  will  still  be  at  the  same  level  in 
both  cylinders.  Hence  the  pressure  of  I  cubic  centi- 
meter of  water  in  the  small  cylinder  balances  the 
pressure  of  100  cubic  centimeters  of  water  in  the  larger 
cylinder.  That  is,  an  additional  pressure  equal -to  the 
weight  of  I  cubic  centimeter  (equals  I  gram)  of  water 


PROPERTIES  OF  BODIES 


117 


has  been  added  to  every  square  centimeter  of  free  sur- 
face of  the  water. 

Suppose  that  instead  of  pouring  water  into  the  larger 
cylinder  a  tight-fitting  piston  had  been  pushed  down  until  it 
was  just  in  contact  with  the  water,  and  then  one  cubic 
centimeter  of  water  had  been  poured  into  the  smaller  tube, 
what  would  have  been  the  upward  pressure  of  the  water  per 
square  centimeter  against  the  piston  in  the  large  cylinder  ? 

What  would  have  been  the  total  upward  pressure  against 
the  piston  ? 

Suppose  that  both  tubes  had  been  fitted  with  pistons,  and 
that  by  pressing  down  upon  the  small  piston  a  weight  had 
been  raised  on  the  large  piston.  What  would  have  been  the 
mechanical  advantage  of  the  small  piston  ?  Through  what 
distance  would  it  have  moved  to  raise  the  large  piston  one 
centimeter  ?  Would  the  general  law  of  machines  apply  to 
this  machine  ? 

The  Hydraulic  Press. — The  machine  just  described 
is  known  as  the  Hydraulic  Press.  It  was  invented  by 
Bramah  in  1796.  The  accompanying  figure  is  from  a 
book  of  that  period.*  The  explanation  given  is  as 


FIG.  39. 

follows :    ' '  The  pump  A  forces  the  water  through  the 
pipe  B  into  the  barrel  C  in  which  it  acts  very  power- 

*Dr.  Thomas  Young's  Lectures  on  Natural  Philosophy,  Vol.  I,  p.  781. 


nS  PHYSICS 

fully  on  the  large  piston  Z),  and  raises  the  bottom  of 
the  press  E. ' '  These  presses  are  sometimes  made  very 
strong  and  capable  of  exerting  enormous  pressures. 

Gravitation  Pressure  Within  a  Liquid. — We  have 
seen  that  in  the  case  of  the  atmosphere  the  weight  of 
the  upper  air  exerts  a  pressure  upon  the  air  near  the 
earth  equivalent  to  about  15  pounds  to  the  square  inch. 
We  know  that  within  the  body  of  the  air  this  pressure 
must  be  equal  in  all  directions,  as  the  most  fragile  soap 
bubble  retains  its  spherical  form.  We  have  also  seen 
that  bodies  lighter  than  air  may  be  driven  upward  by 
this  pressure. 

We  have  seen  that  in  mobile  liquids  any  external 
pressure  upon  the  surface  must  be  the  same  over  the 
whole  surface  to  prevent  motion  in  the  liquid.  The 
same  thing  must,  accordingly,  be  true  of  the  pressure 
exerted  by  the  weight  of  the  upper  layers  of  the  liquid ; 
hence  at  a  given  depth  below  the  surface  of  a  liquid  at 
rest  the  pressure  must  be  everywhere  the  same.  Since 
this  pressure  is  determined  by  the  weight  of  liquid 
above  it,  it  must  increase  as  the  depth  of  the  liquid 
increases. 

Measurement  of  Gravitation  Pressure  Within   a 

Liquid. 

LABORATORY  EXERCISE  38. — A  glass  tube  about  one  centi- 
meter in  bore,  shaped  like  a  Boyle's  tube,  but  open  at  both 
ends,  is  filled  with  water  to  a  depth  of  two  or  three  inches 
on  each  side  of  the  bend.  Pour  a  tall  cylinder,  as  a 
hydrometer  jar,  nearly  full  of  kerosene  or  gasoline  and  lower 
this  tube  into  it  until  the  top  of  the  open  tube  is  below  the 
surface  of  the  liquid  in  the  cylinder,  as  shown  in  Fig.  40. 
Note  the  rise  of  the  water  in  the  long  arm  of  the  tube.  What 
causes  this  rise  ?  Raise  and  lower  the  tube  in  the  liquid  and 
note  the  change  of  height  in  the  column  of  water.  Make 
several  measurements  of  the  distance  from  the  surface  of  the 


PROPERTIES  OF  BODIES  119 

water  in  the  short  arm  to  the  surface  of  the  liquid  in  the 
cylinder  and  to  the  surface  of  the  water  in  the  long  arm.  How 
does  the  pressure  of  the  liquid  upon  the  water  surface  vary  with 
the  depth  ?  Which  is  heavier,  the  liquid  in  the  vessel  or  the 
water  in  the  tube  ?  If  one  cubic  centimeter  of  water  weighs 
a  gram,  what  is  the  downward  pressure  of  the  other  liquid 


FIG.  40. 

in  grams  per  cubic  centimeter  ?  What  is  the  density  of  the 
other  liquid  ?  Measure  out  in  a  graduated  cylinder  fifty 
cubic  centimeters  of  the  liquid  and  weigh  it  on  the  platform 
balance.  What  was  the  error  of  your  estimate  of  its  density  ? 

Pressure  upon  any  Point  within  a  Liquid  is  the 
Same  in  All  Directions. — We  have  seen  from  the  pre- 
ceding experiment  that  the  gravitation  pressure  within 
the  body  of  a  liquid  is  proportional  to  the  depth  below 
the  surface.  We  saw  in  the  case  of  the  oil  globule 
floating  in  another  liquid  that  its  shape  was  spherical, 
hence  the  liquid  pressure  upon  it  must  have  been  equal 
in  all  directions.  We  know,  too,  that  if  this  had  not 
been  the  case  the  oil  would  have  moved  away  from  the 


I2O 


PHYSICS 


greater  pressure  and  toward  the  less.  The  same  thing 
would  be  true  of  any  particle  within  the  water,  hence 
the  conditions  of  equilibrium  in  a  fluid,  either  gas  or 
liquid,  are  that  the  pressures  upon  any  particle  within 
the  fluid  must  be  balanced  on  all  sides.  This  would 
necessarily  follow  if,  as  we  suppose,  the  pressure  upon 
any  surface  is  due  to  the  momentum  of  the  molecules 
striking  against  it,  for  as  many  of  these  molecules  must 
at  any  time  be  moving  in  one  direction  as  in  another. 

Downward  Pressure  of  a  Liquid  Column  Indepen- 
dent of  its  Shape. — That  the  downward  pressure 
within  a  liquid  is  independent  of  the  shape  of  the  liquid 
column  above  the  point  where  the  pressure  is  measured 

follows  from  the  same 
considerations.  To  prove 
this  conclusion  experi- 
mentally, proceed  as  fol- 
lows: 

LABORATORY  EXERCISE  39. 
— Two  lamp  chimneys  of 
different  shapes  are  provided 
with  tight-fitting  corks  in  one 
end  through  which  pass  short 
glass  tubes.  Connect  these 
by  means  of  short  pieces  of 
rubber  tubing  with  ^  lead 
or  glass  T  tube.  Place  the 
lamp  chimneys  with  the  open 
ends  in  a  vessel  of  water, 
and  suck  air  out  of  them 
until  they  stand  about  half 
full  of  water. 

What  supports  the  water 
columns  in  the  lamp  chim- 
neys ?  Is  the  pressure  which 


FIG.  41. 


supports  the  two  columns  the  same  on  each  square  centi- 
meter of  surface  ?    Why  ? 


PROPERTIES  OF  BODIES  121 

Does  the  downward  pressure  of  a  liquid  column  depend 
upon  the  shape  of  the  column  or  only  upon  its  height  ? 

The  downward  pressure  of  a  liquid  upon  a  given  surface 
depends  upon  three  things:  (a)  The  area  of  the  surface;  (d) 
The  height  of  the  liquid  column;  (c)  The  density  of  the 
liquid.  State  the  law  so  as  to  include  these  three  conditions. 

Pressure  of  a  Liquid  upon  the  Sides  of  the  Conf^ 
taining  Vessel. — Since  the  pressure  at  any  point  within 
a  liquid  at  rest  must  be  equal  in  all  directions,  the 
pressure  of  any  liquid  particle  against  the  side  of  the 
containing  vessel  must  be  the  same  as  the  downward 
pressure  of  this  same  particle.  Hence  the  lateral  pres- 
sure upon  any  very  small  area  of  the  side  of  the  vessel 
must  be  the  same  as  the  downward  pressure  upon  an 
equal  area  at  the  same  depth. 

Average  Pressure. — The  total  pressure  upon  a  given 
surface  divided  by  the  area  of  the  surface  is  called  the 
Average  Pressure  over  the  surface. 

The  average  pressure  against  a  square  centimeter  of 
surface  in  the  side  of  a  vessel  is  the  pressure  due  to  the 
depth  of  the  liquid  at  the  middle  point  of  the  area  con- 
sidered. Thus,  if  a  vertical  strip  one  centimeter  wide 
on  the  wall  of  a  vessel  containing  water  be  considered, 
the  pressure  upon  the  first  square  centimeter  measured 
downward  from  the  surface  of  the  liquid  is  .5  gram. 
That  is,  the  lateral  pressure  of  the  liquid  one-half 
centimeter  below  the  surface  is  one-half  gram  per 
square  centimeter.  Upon  the  next  square  centimeter 
below  this  the  lateral  pressure  is  one  arid  a  half  grams. 
What  is  the  total  pressure  upon  such  a  strip  reaching 
six  centimeters  below  the  surface  of  the  water  ?  What 
is  the  area  of  this  total  surface  ?  What  is  the  average 
pressure  upon  it  ?  At  what  depth  is  the  downward 
pressure  equal  to  the  average  lateral  pressure  ? 


122  PHYSICS 

PROBLEMS. — What  is  the  average  lateral  pressure  upon  the 
wall  of  a  vessel  containing  water  to  the  depth  of  ten  centi- 
meters ? 

What  is  the  total  lateral  pressure  upon  a  beaker  ten  centi- 
meters in  circumference  containing  water  to  a  depth  of  eight 
centimeters  ? 

What  is  the  total  pressure  upon  the  sides  of  a  cubical  box 
one  meter  on  each  edge  filled  with  water  ?  What  is  it 
adding  the  atmospheric  pressure  ?  Does  the  box  need  to  be 
made  stronger  on  account  of  the  atmospheric  pressure  ? 

If  a  cubic  foot  of  water  weighs  62^  pounds,  what  is  the 
lateral  pressure  per  square  foot  upon  a  dam  containing  water 
50  feet  deep  ? 

To  what  height  would  the  mercury  stand  in  a  barometer 
tube  50  feet  below  the  surface  of  water  ? 

If  the  cubical  box  one  meter  on  each  edge  be  entirely 
closed  and  filled  with  water  and  then  have  a  tube  one  centi- 
meter square  inserted  in  its  top  and  filled  with  water  to  a 
depth  of  one  meter,  what  additional  pressure  in  grams  per 
square  centimeter  will  be  caused  by  the  water  in  the  tube  ? 
What  will  now  be  the  total  water  pressure  upon  the  six  faces 
of  the  box  ? 

Buoyant  Force  of  a  Liquid. 

Suppose  one  cubic  centimeter  of  water  at  any  depth  below 
the  surface  to  become  solid  without  changing  its  volume  or 
weight,  how  much  would  the  upward  pressure  of  the  liquid 
water  upon  it  exceed  the  downward  pressure  ? 

A  cubical  block  one  centimeter  on  each  edge  is  placed 
with  its  top  face  horizontal  and  four  centimeters  below  the 
surface  of  water  in  a  beaker.  What  is  the  downward  pressure 
of  the  water  upon  its  top  face  ?  What  is  the  upward  pressure 
of  the  water  against  its  bottom  face  ?  What  must  be  the 
weight  of  the  block  to  just  float  in  this  position  ?  If  it 
weighs  five  grams  and  is  supported  by  a  thread,  what  weight 
does  the  thread  support  ?  Will  this  weight  be  different  when 
the  block  is  ten  centimeters  below  the  surface  ? 

If  the  block  were  a  rectangular  prism  having  ends  of  one- 
fourth  square  centimeter  area  and  a  height  of  four  centimeters, 
its  volume  would  be  one  cubic  centimeter.  If  it  were  sup- 
ported vertically  in  the  water,  what  would  be  the  buoyant 
force  of  the  water  upon  it  ?  What  would  be  the  buoyant 


PROPERTIES  OF  BODIES 


123 


force  of  the  water  upon  it  if  it  were  lying  on  its  side  in  the 
water  ? 

What  volume  of  water  weighs  as  much  as  the  loss  of 
weight  of  the  block  in  water  ? 

Loss  of  Weight  of  a  Body  Immersed  in  Water. 

LABORATORY  EXERCISE  40. — Attach  a  thread  to  a  piece  of 
metal  or  other  solid  having  a  volume  of  several  cubic  centi- 
meters. Lower  the  solid  into  a  graduated  cylinder  of  water 
and  note  the  increase  of  volume  when  the  solid  is  immersed 
in  the  water.  Record  the  volume  of  the  solid. 

Place  the  platform  balance  on  a  box  or  a  board  supported 
on  blocks  through  which  two  holes  have  been  bored  at  a 
distance  apart  equal  to  the  distance  between  the  centers  of 
the  pans.  From  the  ends  of  the  lever  arms  directly  below 
the  center  of  one  of  the  pans,  attach  the  thread  by  means  of 
a  bent-wire  hook,  and  let  the  solid  swing  just  above  the 
table.  Counterpoise  by  means  of  weights  on  the  other  pan. 


FIG.  42. 

Place  a  beaker  of  water  so  that  the  solid  will  be  suspended 
immersed  in  the  water,  and  add  known  weights  to  the 
balance  pan  until  equilibrium  is  produced.  These  weights 
represent  the  loss  of  weight  of  the  solid  in  water.  Record 


124 


PHYSICS 


this  loss  of  weight.  How  does  it  compare  with  the  weight 
of  a  volume  of  water  equal  to  the  volume  of  the  body  ? 

Place  the  beaker  of  water  on  one  balance  pan  and 
counterpoise  with  weights  on  the  other.  Suspend  the  solid 
just  used  so  that  it  will  swing  immersed  in  the  water  without 
touching  the  beaker.  What  additional  weight  does  the 
immersed  body  give  to  the  water  ?  How  does  the  gain  in 
weight  of  the  water  compare  with  the  loss  of  weight  of  the 
body  ?  How  many  cubic  centimeters  of  water  would  have 
to  be  poured  into  the  beaker  to  increase  its  weight  as  much 
as  it  is  increased  by  the  immersed  body  ? 

A  tin  can  or  other  vessel  holding  about  a  pint  has  one 

edge  bent  down  at  the  top 
forming  a  lip,  and  has  a  spout 
two  or  three  inches  long 
soldered  to  this  lip  to  carry 
off-  the  overflow.  Place  this 
can  on  the  balance  with  the 
end  of  the  spout  projecting 
beyond  the  side  of  the  pan, 
and  set  a  vessel  on  the  table 
beside  the  balance  to  catch 
the  overflow.  Fill  the  can 
with  water  until  some  over- 
flows, and  then  counterpoise 
it.  Attach  as  large  a  solid  as 
can  be  conveniently  used  to 
FlG<  43>  a  thread  and  lower  it  into  the 

water  until  it  is  immersed,  allowing -the  water  to  overflow 
into  an  empty  vessel.  Have  you  changed  the  weight  of  the 
can  of  water  ?  Why  ? 

Weigh  the  overflowed  water  and,  assuming  that  one  cubic 
centimeter  of  water  weighs  a  gram,  calculate  the  volume  of 
the  body  from  the  weight  of  the  displaced  water.     Weigh 
the  solid  and  calculate  its  density. 
Floating  Bodies. 

LABORATORY  EXERCISE  41. — Weigh  a  small  block  of  wood. 
Place  a  vessel  of  water  upon  one  pan  of  the  balance,  counter- 
poise it,  and  place  the  block  in  the  water.  Does  it  add  its 
own  weight  to  the  weight  of  the  water  ? 

Place  the   overflow  vessel    upon  the  balance.      Fill   with 


PROPERTIES  OF  BODIES  125 

water  and  counterpoise.  Place  the  block  in  the  water  and 
catch  the  overflow  in  an  empty  vessel.  What  weight  of 
water  has  apparently  overflowed  ?  Weigh  the  overflow  and 
see  if  your  conclusion  is  correct.  A  floating  body  displaces 
what  weight  of  water  ? 

Principle  of  Archimedes. — About  250  B.C.,  Archi- 
medes, in  Sicily,  stated  the  principle  which  has  since 
been  known  by  his  name.  It  is  as  follows:  "A  body 
suspended  in  a  fluid  apparently  loses  as  much  weight  as 
is  equal  to  the  weight  of  the  quantity  of  fluid  which  it 
displaces. ' '  (Does  this  statement  express  the  results 
of  the  preceding  experiments  ?) 

This  gives  us  a  very  accurate  method  of  determining 
the  volume  of  a  body.  With  a  good  balance  the  loss 
of  weight  of  a  small  body  immersed  in  water  can  be 
determined  to  within  a  milligram,  which  corresponds  to 
a  volume  of  .001  cubic  centimeter.  No  other  method 
of  measuring  the  volume  is  so  accurate  as  this. 

Density  and  Specific  Gravity  of  Liquids  and  Solids. 
— The  specific  gravity  of  liquids  and  solids  is  generally 
referred  to  water  as  a  standard.  This  would  make  the 
specific  gravity  of  water  equal  to  unity  Since  one 
cubic  centimeter  of  water  weighs  very  approximately 
one  gram,  the  density  of  water  in  grams  per  cubic 
centimeter  is  also  equal  to  unity.  Hence  the  density 
of  any  body  expressed  in  grams  per  cubic  centimeter 
and  its  specific  gravity  referred  to  water  are  numerically 
equal.  If  the  density  were  measured  in  pounds  per 
cubic  foot,  the  density  of  water  would  be  62 £  and  con- 
sequently would  not  be  numerically  the  same  as  its 
specific  gravity. 

Measurement  of  Density  by  Principle  of  Archi- 
medes. 

LABORATORY  EXERCISE  42. — Suspend  a  piece  of  metal  or  a 


126  PHYSICS 

stone  below  the  balance  pan  and  counterpoise  as  in  Exercise 
40.  Place  a  beaker  of  water  so  that  the  solid  is  immersed 
in  it,  and  find  its  loss  of  weight.  Calculate  the  volume  .of 
the  solid.  Find  its  loss  of  weight  in  kerosene  or  some  other 
liquid,  and  calculate  the  density  of  this  liquid. 

Weigh  the  solid  and  calculate  its  density. 

Place  the  overflow  vessel  full  of  water  so  that  the  water 
will  flow  over  into  a  counterpoised  vessel  on  one  pan  of  the 
balance.  Place  a  block  of  wood  on  the  water  and  determine 
its  weight  from  the  weight  of  the  overflow  water.  With  a 
long  pin  or  needle  force  the  rJlock  below  the  surface  of  the 
water,  and  calculate  its  volume  by  means  of  the  overflow 
water.  Calculate  the  density  of  the  block. 

Use  of  Specific-gravity  Bottle. 

LABORATORY  EXERCISE  43.* — Find  the  cubical  content  of 
a  specific -gravity  bottle  by  weighing  first  the  bottle  and  then 
the  bottle  filled  to  a  marked  height  with  water.  Pour  out  the 
water  and  fill  to  the  same  height  with  another  liquid  and 
weigh  again.  Calculate  the  density  of  the  other  liquid. 

Weigh  out  about  20  grams  of  shot  and  pour  into  the 
bottle.  Fill  with  water  to  the  previous  mark  and  weigh. 
What  weight  of  water  does  the  bottle  contain  ?  What 
volume  of  shot  does  it  contain  ?  What  is  the  density  of  the 
shot? 

PROBLEMS. — How  much  more  will  a  liter  of  water  weigh 
in  a  vacuum  than  in  the  air  ? 

A  piece  of  brass  weighs  85  grams  in  the  air,  75  grams  in 
water,  and  77  grams  in  another  liquid.  What  is  the  volume 
of  the  brass  ?  What  is  its  density  ?  What  is  the  density  of 
the  other  liquid  ? 

An  iron  ball  (density  7.5)  weighs  1000  grams  in  air. 
What  will  it  weigh  in  kerosene  of  density  .  8  ? 

The  density  of  cork  is  .24.  What  will  be  the  loss  of 
weight  in  air  of  one  kilogram  of  cork  ? 

Calculate  the  displacement  of  a  balloon  which  with  its 
contents  weighs  100  pounds  and  by  which  you  could  be 
raised  from  the  ground. 

*-This  exercise  lias  no  special  bearing  upon  the  theory  of  Physics,  and 
may  be  omitted  if  desired. 


PROPERTIES  OF  BODIES  127 

SOLID   STATE 

PROPERTIES   OF   SOLIDS 

Change  from  Liquid  to  Solid  State. — Any  known 
liquid  may  be  changed  to  the  solid  form  by  lowering 
its  temperature  sufficiently.  Thus,  water  when  suffi- 
ciently cooled  becomes  ice.  Mercury  solidifies  at  a 
temperature  lower  than  the  freezing-point  of  water,  and 
the  other  common  metals  at  much  higher  temperatures. 
The  gases  of  the  atmosphere  change  to  liquids  and 
then  to  solids  only  at  very  low  temperatures. 

As  the  temperature  of  a  liquid  is  lowered  its  viscosity 
increases.  In  some  substances  this  change  is  contin- 
uous until  a  condition  of  rigidity  is  reached  and  we  call 
the  substance  a  solid. 

In  other  cases,  solidification  begins  at  certain  centers 
(perhaps  upon  other  solid  particles  already  within  the 
liquid),  and  spreads  through  the  liquid.  In  this  case, 
the  particles  of  the  liquid  which  come  to  rest  in  the 
solid  form  are  held  to  the  surfaces  of  the  solid  masses 
already  formed. 

Structure  of  Solids. 

LABORATORY  EXERCISE  44. — Melt  a  piece  of  sealing-wax 
in  a  convenient  vessel  and  allow  it  to  solidify  by  cooling. 
Note  that  it  changes  gradually  from  a  liquid  to  a  solid, 
becoming  more  and  more  viscous  until  finally,  while  still 
soft,  it  may  be  pressed  into  a  form  which  it  will  permanently 
retain.  After  it  has  solidified  it  is  seen  to  be  without  any 
visible  structure,  any  one  particle  appearing  exactly  like  any 
other. 

Solid  bodies  which,  like  sealing-wax  and  glass,  show  no 
regular  internal  structure  are  said  to  be  Amorphous. 

Melt  a  quantity  of  sulphur  in  a  glass  or  porcelain  vessel, 
and  after  it  has  become  a  clear  liquid  set  it  aside  and  allow 


128  PHYSICS 

it  to  cool  slowly  without  disturbance.  When  it  is  about 
half  solidified  pour  off  the  remaining  liquid  and  note  the 
structure  of  the  solid  part.  It  will  be  seen  to  be  made  up 
of  small  bodies  called  crystals.  Examine  these  and  deter- 
mine if  they  bear  any  general  resemblance  to  each  other. 

Bodies  which,  like  sulphur,  solidify  in  the  form  of  crystals 
are  called  Crystalline.  The  crystalline  form  is  much  more 
common  in  nature  than  the  amorphous. 

There  is  still  another  form  of  solid  structure  known  as  the 
Cellular.  This  includes  the  solid  parts  of  plant  and  animal 
bodies,  and  is  built  up  from  the  living  cell. 

Properties  of  Crystalline  Solids. 

LABORATORY  EXERCISE  45. — Examine  specimens  of  differ- 
ent crystalline  substances  and  notice  that  in  general  crystals 
are  bounded  by  plane  faces  which  make  definite  angles  with 
each  other  in  all  crystals  of  the  same  substance.  Notice 
that  a  block  of  mica  is  bounded  on  two  opposite  faces  by 
these  crystalline  planes,  and  that  it  can  be  separated  into 
very  thin  parallel  sheets,  each  sheet  having  naturally  polished 
surfaces. 

These  natural  planes  of  separation  in  a  crystal  are  called 
Cleavage  Planes.  They  indicate  that  the  molecules  of  a 
crystal  are  not  spaced  at  equal  distances  in  all  directions. 

Look  through *a  crystal  of  Iceland  spar  at  a  pin-hole  in  a 
piece  of  cardboard  held  against  one  side  of  the  crystal. 
Note  that  in  some  positions  you  can  apparently  see  two  pin- 
holes,  and  that  the  apparent  distance  between  them  varies 
with  the  direction  of  sight  through  the  crystal. 

Look  at  a  lighted  window  through  two  tourmaline  crystals 
mounted  in  the  tourmaline  tongs.  Rotate  one  of  the 
crystals  around  the  line  of  sight  and  note  that  in  certain 
positions  it  shuts  off  the  light  which  comes  through  the 
other  crystal,  while  in  other  positions  it  allows  it  to  pass 
through. 

All  of  these  observations  indicate  that  in  crystals  some  of 
the  physical  properties  are  different  in  different  directions 
through  the  crystal.  The  same  thing  is  true  for  many  other 
properties.  Thus  if  a  sphere  be  turned  out  of  a  crystalline 
substance  and  be  immersed  in  a  liquid  and  put  under  heavy 
pressure,  though  the  pressure  is  necessarily  equal  in  all 
directions,  the  compression  will  be  greater  in  some  directions 


PROPERTIES  OF  BODIES  129 

than  in  others,  showing  that  the  elasticity  of  compression  of 
the  crystal  is  different  in  different  directions. 

If  a  sphere  be  turned  from  a  crystal  and  immersed  in  an 
acid  solution  which  will  etch  away  the  crystal,  the  crystal 
will  not  remain  spherical,  but  will  be  gradually  etched  down 
to  its  original  form,  showing  again  that  cohesion  is  different 
in  different  directions  through  the  crystal. 

Isotropic  and  Anisotropic  Bodies. — Bodies  in  which 
all  physical  properties  are  the  same  in  all  directions 
through  the  body  are  said  to  be  Isotropic.  Bodies  in 
which  some  of  the  physical  properties  vary  with  direc- 
tion are  called  Anisotropic. 

Crystals  are  anisotropic  bodies.  Amorphous  solids, 
as  well  as  liquids  and  gases,  are  isotropic. 

Equilibrium  of  Solid  and  Liquid  States. — If  a  vessel 
containing  broken  ice  and  water  be  placed  where  it  can 
neither  receive  nor  give  off  heat,  the  total  quantity  of 
ice  and  water  will  remain  the  same.  It  is  believed  that 
in  this  condition  molecules  are  constantly  escaping  from 
the  ice  to  the  water,  and  other  molecules  are  constantly 
striking  against  the  ice  surfaces  and  being  held  fast  by 
cohesion.  As  long  as  the  total  quantity  of  heat  in  the 
whole  mass  remains  unchanged,  as  many  molecules 
must  go  into  the  solid  state  as  into  the  liquid  state  in 
the  same  time. 

Cohesion  between  Solid  Surfaces. 

LABORATORY  EXERCISE  46. — Press  together  tightly  with  a 
rotary  motion  of  one  surface  upon  the  other  two  plane, 
polished  glass  surfaces,  and  note  the  force  required  to  pull 
them  apart. 

Do  the  same  for  two  freshly  cut  plane  lead  surfaces. 
What  apparently  holds  the  surfaces  together?  (N. B.  The 
surfaces  are  held  together  with  a  very  considerable  pressure 
in  the  exhausted  receiver  of  an  air-pump.  What  possible 
cause  of  the  pressure  does  this  exclude  ?) 


130  PHYSICS 

In  welding  metal  surfaces  they  are  first  heated  to 
soften  the  metal  and  are  then  hammered  into  close 
contact  with  each  other,  after  which  they  cling  together 
on  account  of  the  cohesion  between  their  molecules. 

FRICTION   BETWEEN   SOLID   SURFACES 

Cause  of  Friction. — The  resistance  which  one  solid 
surface  meets  with  in  moving  over  another  is  called 
Friction.  Friction  is  always  accompanied  by  a  wear- 
ing away  of  the  surfaces,  and  is  in  large  part  due  to 
the  force  required  to  break  off  the  small  projecting 
particles  from  the  surface.  Polishing  the  surfaces  of 
contact  accordingly  reduces  the  friction  between  them. 

When  surfaces  are  rough  there  is  no  regularity  in  the 
friction  between  them,  but  the  friction  between  smooth 
surfaces  follows  definite  laws.  If  the  surfaces  are 
highly  polished  and  of  the  same  material  (as  in  Exer- 
cise 46),  the  cohesion  is  often  so  great  between  them 
that  one  surface  can  scarcely  be  moved  over  the  other 
at  all. 

Coefficient  of  Friction. 

LABORATORY  EXERCISE  47. — For  experiments  on  friction  a 
straight-grained  pine  board  about  a  meter  long  and  20  or  30 


FIG.  44. 

centimeters  wide  should  have  one  face  carefully  planed  and 
sandpapered.  This  board  should  be  kept  only  for  friction 
experiments. 


PROPERTIES  OF  BODIES  131 

Several  blocks  of  different  kinds  of  wood  about  20  by  10 
by  5  centimeters  should  be  prepared  and  carefully  smoothed. 
These  may  be  cut  from  2  X  4-inch  or  2  x  6-inch  scantling, 
and  should  have  screw  hooks  fastened  into  the  center  of  one 
end. 

Place  the  board  on  a  table  with  the  smooth  face  upward, 
lay  one  of  the  blocks  on  its  smooth  side  on  the  board,  place 
a  weight  of  several  pounds  or  kilograms  on  the  block,  and 
by  means  of  a  spring  balance,  weighing  to  ounces  or  other 
small  units  and  attached  to  the  hook  by  a  cord,  pull  the 
block  with  uniform  motion  along  the  board  and  note  the 
reading  of  the  balance.  Why  is  it  important  that  the  cord 
should  be  kept  parallel  to  the  board  ?  After  the  block  is 
once  in  motion,  does  the  balance  indicate  a  greater  pull  when 
the  block  is  drawn  rapidly  along  the  board  than  when  it  is 
drawn  slowly  ?  Why  should  the  balance  reading  be  greater 
when  the  motion  of  the  block  is  being  accelerated  ? 

Turn  the  block  on  edge,  load  it  with  the  same  weight  as 
before,  and  repeat  the  experiment.  Does  the  amount  of 
friction  vary  with  the  area  of  the  contact  surfaces  ? 

Lay  the  block  on  its  side  and  find  the  force  required  to 
pull  it  with  uniform  speed  under  different  loads.  Tabulate 
your  results,  giving  the  load  (including  the  weight  of  the 
block),  and  the  pull  on  the  balance  for  several  different  loads. 

The  coefficient  of  friction  has  been  defined  as  the  quotient 
of  the  force  parallel  to  the  surfaces  of  contact  divided  by  the 
total  pressure  normal  to  these  surfaces.  In  your  experi- 
ments it  is  the  pull  on  the  balance  divided  by  the  total 
weight  of  the  block  and  its  load  expressed  in  the  same  units. 
Calculate  this  coefficient  for  all  of  your  experiments.  What 
is  the  average  of  your  determinations  ? 

Determine  the  coefficient  of  friction  between  surfaces  of 
two  different  kinds  of  wood.  \ 

Coulomb's  Laws  of  Friction, — The  first  careful  meas- 
urements of  friction  were  made  by  Coulomb  in  1781. 
Coulomb's  Laws  of  Friction  may  be  stated  as  follows: 
The  friction  between  two  solid  surfaces  is  independent 
of  the  extension  of  the  surfaces  of  contact,  is  proportional 
to  the  pressure,  and  independent  of  the  velocity  of  motion. 
Are  these  statements  borne  out  by  your  experiments  ? 


1 32  PHYSICS 

The  above  laws  are  subject  to  considerable  modifica- 
tion. We  have  seen  that  when  the  surfaces  are  brought 
near  enough  to  allow  cohesion  to  act  between  them  the 
friction  may  depend  greatly  upon  the  area  of  the  sur- 
faces of  contact. 

If  your  board  be  rested  only  upon  supports  at  the 
ends  and  a  heavy  load  be  drawn  lengthwise  of  it,  the 
board  will  bend  downward  in  the  middle,  and  the  load 
will  have  to  be  drawn  up-hill.  The  deformation  of  a 
surface  under  a  heavy  load  is  one  of  the  principal 
causes  of  the  resistance  to  motion  along  it. 

Rolling  Friction. — When  a  cylinder  or  a  sphere  is 
rolled  over  a  plane  surface  there  is  no  slipping  of  one 
surface  upon  the  other,  and  consequently  no  friction  of 
the  same  kind  as  between  sliding  surfaces.  In  this 
case,  the  principal  resistance  to  motion  is  in  the 
deformation  of  the  surface.  Thus  a  heavy  cylinder 
rolling  over  a  flat  surface  always  causes  a  depression  in 
the  surface,  and  the  cylinder  must  be  constantly  rolled 
up-hill.  If  this  depression  is  great  enough  to  cause  a 
slipping  of  the  cylinder  upon  the  flat  surface,  ordinary 
friction  will  result. 

The  freedom  from  ordinary  friction  in  rolling  motion 
has  led  to  the  extensive  use  of  ball  bearings  in  bicycles 
and  other  machines. 

The  friction  of  a  shaft  in  its  bearing  is  not  rolling 
friction.  In  this  case,  the  shaft  rolls  upward  on  one 
side  of  its  bearing  until  it  can  roll  no  higher  and  then 
slips  on  the  side  of  the  bearing. 

Use  of  Lubricants. — Since  the  viscosity  between 
liquid  surfaces  is  less  than  the  friction  between  solid 
surfaces,  liquids  are  frequently  placed  between  solid 
surfaces  to  lessen  their  friction.  If  the  moving  surface 


PROPERTIES  OF  BODIES  133 

could  be  entirely  floated  upon  the  liquid,  solid  friction 
would  be  entirely  replaced  by  viscosity,  but  this  is  not 
often  practicable. 

Sometimes  amorphous  solids,  as  graphite,  are  used 
as  lubricants.  In  graphite  the  cohesion  between  the 
small  particles  is  so  slight  that  the  friction  between  two 
surfaces  covered  with  graphite  is  much  diminished. 

ELASTICITY   OF   SOLIDS 

Elasticity  of  Compression. — Solids,  like  liquids, 
offer  great  resistance  to  compression  of  volume.  This 
compressibility  has  been  accurately  measured  in  only 
a  few  solids.  In  general,  solids  are  less  compressible 
than  liquids.  Glass  is  about  one  sixteenth  as  com- 
pressible as  water,  or  about  as  compressible  as  mercury. 
Brass,  copper,  and  steel  are  less  compressible  than 
glass. 

It  has  already  been  mentioned  that  the  compressi- 
bility of  crystals  varies  in  different  directions  through 
the  crystal,  so  that  no  definite  coefficient  of  compressi- 
bility can  be  given  for  crystalline  solids. 

Rigidity. — In  addition  to  having  a  greater  elasticity 
of  volume  than  liquids,  solids  also  have  elasticity  of 
form,  or  rigidity.  The  magnitude  of  rigidity  varies 
greatly  in  different  solids,  being  very  great  in  steel  and 
small  in  India  rubber  or  jelly. 

The  rigidity  of  a  body  may  be  measured  by  the  force 
required  to  bend  it,  to  stretch  it,  to  twist  it,  or  to  com- 
press it  in  one  or  two  dimensions.  According  as  we 
use  one  or  the  other  of  these  methods  we  get  different 
numbers  to  represent  the  rigidity  of  a  body. 

Hooke's  Law. — All  measurements  of  the  elasticity 
of  solids  are  based  upon  Hooke's  Law,  stated  in  1678, 


i34  PHYSICS 

according  to  which  the  amount  of  change  of  shape  is 
proportional  to  the  distorting  force;  i.e.,  the  elongation 
is  proportional  to  the  stretching  force,  and  the  like. 
This  law  is  now  known  not  to  apply  accurately  to 
stretching  forces,  and  probably  does  not  apply  with 
perfect  accuracy  to  distorting  forces  of  any  kind. 
Within  the  limits  of  ordinary  experimental  accuracy, 
however,  Hooke's  Law  applies  to  rigidity  just  as  the 
similar  law  of  Boyle  applies  to  compressibility  of  gases. 
Thus,  if  a  wire  one  meter  long  be  stretched  one  milli- 
meter by  a  weight  of  one  kilogram,  it  will  be  stretched 
two  millimeters  by  a  weight  of  two  kilograms.  If  a 
beam  supported  at  its  ends  be  depressed  one  inch  by  a 
load  of  one  hundred  pounds,  it  will  be  depressed  two 
inches  by  a  load  of  two  hundred  pounds. 

Limits  of  Perfect  Elasticity. — We  have  defined  as 
' '  perfectly  elastic  ' '  those  bodies  in  which  a  given 
pressure  always  produces  the  same  change  of  form  or 
change  of  volume.  In  this  sense  the  rigidity  of  most 
solids  is  only  perfect  within  comparatively  narrow 
limits.  If  the  body  be  stretched  or  bent  beyond  these 
limits,  it  is  either  broken  or  has  its  shape  permanently 
changed. 

If  a  body  breaks  under  a  pressure  before  it  has  its 
shape  permanently  changed,  it  is  said  to  be  brittle.  If 
it  assumes  a  permanent  change  of  shape,  it  is  said  to  be 
malleable  or  plastic  or  ductile.  Metals  are  usually 
malleable,  but  may  be  made  brittle  by  hardening. 

Steel  has  the  widest  range  of  perfect  elasticity  of  any 
known  metal.  The  steel  piano  wire  which  is  used  in 
deep-sea  soundings  stretches  by  one  eighty-sixth  of  its 
original  length  before  it  becomes  permanent!^  elon- 
gated. In  cork,  India  rubber,  and  jellies  the  limits  of 


PROPERTIES  OF  BODIES  135 

perfect  elasticity  are  proportionally  wider.  An  India- 
rubber  band  may  stretch  to  eight  times  its  original 
length  and  return  to  almost  its  original  length  when 
the  stretching  force  is  removed.  The  limits  of  perfect 
elasticity  of  lead  and  putty  are  very  small. 

The  elasticity  of  a  body  is  weakened  by  repeated 
stretching  or  bending.  A  vibrating  tuning  fork  comes 
to  rest  more  quickly  after  having  been  kept  in  vibration 
for  a  long  time  than  after  a  period  of  rest. 

Change  of  Density  in  Solids. — Malleable  metals 
may  have  their  densities  considerably  changed  by 
hammering,  compression,  or  stretching.  The  density 
of  gold  is  increased  in  coining  by  over  a  half  of  one 
per  cent,  and  the  density  of  silver  is  increased  in  the 
same  way  by  more  than  four  per  cent.  The  density 
of  a  wire  may  be  decreased  by  permanently  stretching 
it. 

Elastic  Impact. — We  may  now  sefe  how  two  elastic 
balls  may  rebound  after  collison  with  each  other.  In 
striking  against  each  other  the  balls  are  at  first 
flattened,  but  on  account  of  their  rigidity  they  quickly 
return  to  their  original  shape.  In  doing  this  they 
mutually  push  each  other  apart.  If  their  elasticity  is 
perfect,  they  do  as  much  work  upon  each  other  in 
recovering  from  the  distortion  as  while  the  distortion 
was  taking  place,  consequently  they  have  the  same 
momentum  and  the  same  kinetic  energy  after  impact 
as  before.  If  not  perfectly  elastic,  some  work  is  used 
up  in  permanently  changing  the  shape  of  the  balls,  and 
while  their  momentum  after  impact  is  the  same  as 
before,  their  kinetic  energy  may  be  less.  Thus  two 
equal  balls  of  putty  moving  in  opposite  directions  with 
equal  velocities  will  cling  together  and  come  to  rest 


PHYSICS 


after  collision.  Since  the  algebraic  sum  of  their 
momentums  before  impact  was  zero,  it  remains  un- 
changed, but  their  kinetic  energy  has  disappeared. 
Has  the  energy  done  work  upon  the  balls  ? 


PART  HI 

HEAT 

ORIGIN   OF    OUR   KNOWLEDGE   OF   HEAT 

The  Temperature  Sense. — Our  knowledge  of  heat  is 
derived  in  the  first  place 'from  the  Temperature  Sense. 
A  large  number  of  highly  specialized  nerves,  called 
Temperature  Nerves,  are  distributed  to  the  skin  over 
the  whole  body,  and  these  enable  us  to  tell  whether 
objects  which  come  in  contact  with  our  bodies  are 
warmer  or  colder  than  the  skin. 

The  temperature  sense  also  enables  us  to  tell  within 
rather  narrow  limits  which  of  two  bodies  of  the  same 
kind  is  the  warmer,  but  it  does  not  enable  us  to  judge 
of  the  temperature  of  bodies  of  different  kinds.  A 
piece  of  iron  and  a  piece  of  wood  may  produce  very 
different  temperature  sensations  in  our  bodies  when  we 
know  them  to  be  actually  of  the  same  temperature. 

The  temperature  sense,  accordingly,  gives  us  knowl- 
edge of  the  temperature  of  surrounding  objects  as 
related  to  our  bodies,  but  it  does  not  enable  us  to  com- 
pare the  temperatures  of  different  bodies,  or  even  to 
tell  accurately  how  much  warmer  or  colder  another 
object  is  than  our  bodies. 

Definition  of  Heat. — The  name  heat  has  been  given 
to  both  the  sensation  and  to  the  physical  cause  of  the 

i37 


138  PHYSICS 

sensation.  In  the  study  of  Physics  we  define  heat  as 
the  physical  condition  which  may  give  rise  to  the  sensa- 
tion of  warmth  in  our  bodies. 

Other  Means  of  Recognizing  Heat. — Heated  bodies 
may  be  recognized  by  us  in  several  other  ways  than 
by  means  of  the  temperature  sense.  We  have  seen 
that  gases  expand  on  heating,  and  that  the  amount  of 
their  expansion  may  be  used  as  a  measure  of  their 
change  of  temperature.  We  have  also  seen  that  solids 
may  be  changed  to  liquids  and  liquids  to  gases  by 
simply  increasing  their  temperatures.  We  also  know 
that  many  bodies  may  be  made  luminous  by  heating, 
and  that  practically  all  of  our  appliances  for  artificial 
light  depend  upon  the  use  of  such  luminous  bodies. 

SOURCES   OF    HEAT 

Importance  of  Sun's  Radiation. — The  principal 
.source  of  heat  upon  the  earth  is  the  radiation  from  the 
sun.  The  nature  of  this  radiation  can  be  better  inferred 
after  we  have  discussed  more  fully  the  physics  of  the 
Luminiferous  Ether. 

Chemical  Sources  of  Heat. — Besides  radiation,  the 
most  important  source  of  heat  is  chemical  action, 
especially  combustion  with  oxygen.  Many  substances, 
including  most  of  the  materials  of  vegetable  and  animal 
bodies,  will,  when  sufficiently  heated,  combine  with 
oxygen  to  form  new  chemical  compounds.  The  heat 
derived  from  this  chemical  combination  may  be  many 
times  as  great  as  the  heat  required  to  start  the  com- 
bination in  the  first  place,  and  this  excess  of  heat  may 
be  made  useful  to  us  in  many  ways. 

Mechanical  Production  of  Heat. — Bodies  may  also 
be  heated  by  percussion,  friction,  compression,  and  the 


HEAT  139 

like.  Thus  a  piece  of  iron  may  be  made  red  hot  by 
hammering  it  upon  an  anvil.  A  piece  of  wire  held  in 
the  fingers  and  rapidly  bent  backwards  and  forwards 
soon  becomes  heated  at  the  place  of  bending.  Bodies 
are  heated  by  rubbing  one  upon  another,  and  savages 
sometimes  build  fires  by  the  friction  of  one  piece  of  dry 
wood  upon  another.  Gases  are  heated  by  compression, 
so  that  in  the  process  of  inflating  a  bicycle  tire  the 
pump  soon  becomes  sensibly  warmed.  In  fact,  when 
work  is  done  upon  a  body  in  any  way  without  increas- 
ing its  kinetic  or  potential  energy  the  body  is  usually 
heated. 

NATURE  OF  HEAT 

The  Caloric  Theory. — The  modern  theory  of  heat  is 
based  upon  the  discovery  of  definite  relations  between 
the  expenditure  of  energy  and  the  production  of  heat, 
and  the  disappearance  of  heat  in  the  production  of 
work.  Before  this  discovery  was  made,  heat  was  sup- 
posed to  be  an  invisible,  imponderable  fluid,  which 
could  of  itself  pass  from  a  hot  to  a  cold  body,  and 
which  could  be  forced  from  one  body  to  another  by 
percussion,  compression,  and  the  like.  When  a  suffi- 
cient quantity  of  this  fluid  had  penetrated  a  solid  body, 
the  body  became  a  liquid,  and  a  still  greater  quantity 
of  the  fluid  mixed  with  the  molecules  of  matter  caused 
the  body  to  assume  the  gaseous  form.  The  name 
Caloric  was  given  to  this  hypothetical  fluid.  Thus, 
water  was  supposed  to  consist  of  ice  and  caloric,  steam 
of  water  and  more  caloric. 

Count  Rumford's  Experiment. — The  first  experi- 
mental investigation  which  gave  any  accurate  knowl- 
edge as  to  the  true  nature  of  heat  was  made  by  Count 


1 40  PHYSICS 

Rumford  in  1798.  While  engaged  in  the  boring  of 
brass  cannon  in  the  arsenal  at  Munich,  Rumford  was 
impressed  by  the  great  quantity  of  heat  given  off  during 
the  process.  To  determine,  if  possible,  the  source  of 
this  great  quantity  of  heat,  Rumford  caused  to  be  turned 
out  a  hollow  brass  cylinder  about  25  centimeters  long 
and  1 6  centimeters  in  external  diameter  in  which  he 
placed  a  blunt  steel  borer  made  to  bear  against  the 
bottom  with  a  pressure  of  about  10,000  pounds,  and 
set  it  in  rotation  by  means  of  horse-power.  He  found 
in  this  way  that  a  great  quantity  of  heat  could  be  pro- 
duced in  the  wearing  away  of  a  very  small  quantity  of 
metal,  and  that  there  seemed  to  be  no  relation  between 
the  quantity  of  metal  bored  out  and  the  quantity  of  heat 
produced.  He  found,  however,  that  when  his  metal 
cylinder  was  placed  in  water  and  the  borer  kept  in 
constant  rotation  the  heat  was  generated  at  a  uniform 
rate.  He  concluded  that  one  horse  working  in  turning 
his  drill  could  in  two  and  a  half  hours  heat  to  the  boil- 
ing-point 26.58  pounds  of  ice-cold  water,  or  about  10 
pounds  an  hour. 

In  reasoning  upon  the  results  of  his  experiments  he 
says :  * '  It  is  hardly  necessary  to  add  that  anything  which 
an  insulated  body  or  system  of  bodies  can  continue  to 
furnish  without  limitation  can  not  possibly  be  a  material 
substance  ;  and  it  appears  to  me  to  be  extremely  difficult, 
if  not  quite  impossible,  to  form  any  distinct  idea  of 
anything  capable  of  being  excited  and  communicated  in 
the  manner  the  heat  was  excited  and  communicated  in 
these  experiments,  except  it  be  Motion. ' ' 

Davy's  Experiments. — Following  Rumford 's  ex- 
periment, Sir  Humphry  Davy  succeeded  in  melting 
two  pieces  of  ice  by  friction  between  their  surfaces  in  a 


HEAT  141 

vacuum  at  a  temperature  lower  than  the  freezing-point 
of  water,  showing  conclusively  that  the  heat  could  not 
have  been  communicated  from  surrounding  bodies,  and 
must  have  come  from  the  rubbing  together  of  the  ice 
surfaces.  Rumford  and  Davy  both  believed  heat  to 
be  due  to  the  motion  of  the  small  particles  or  molecules 
of  the  hot  body,  and  that  when  heat  was  produced  by 
friction,  percussion,  and  the  like,  the  motion  of  the 
larger  masses  was  transformed  into  the  motion  of  the 
smaller  particles.  Accordingly,  the  physicists  of  that 
period  undertook  to  determine  experimentally  the  rela- 
tion between  the  amount  of  motion  destroyed  and  the 
amount  of  heat  produced.  This  proved  a  very  difficult 
problem.  Since  the  time  of  Newton  momentum  had 
been  taken  to  represent  the  measure  of  the  quantity  of 
motion  of  a  moving  body,  and  physicists  naturally 
looked  for  a  quantitative  relation  between  the  loss  of 
momentum  and  the  gain  of  heat.  No  such  relation  was 
found  to  exist.  Energy,  as  a  physical  quantity,  had 
not  yet  been  discovered,  and  the  relation  between  work 
and  energy  was  consequently  unknown.  *yC 

Carnot's  Theory. — Twenty-five  years  after  Rum- 
ford's  experiment,  Sadi  Carnot,  in  France,  made  many 
important  investigations  regarding  the  working  condi- 
tions of  steam-engines.  At  this  time  the  steam-engine 
had  been  in  use  about  fifty  years,  but  apparently  no 
one  had  thought  of  any  relation  between  the  work  done 
by  an  engine  and  the  heat  lost  by  the  steam  during  its 
production.  Carnot  made  the  observation  that  the 
steam  was  cooled  more  in  driving  the  piston  against 
an  external  pressure  than  when  no  work  was  done  by 
the  piston,  so  that  much  more  heat  was  given  up  in 
the  condensation  of  the  steam  when  it  was  simply 


142  PHYSICS 

blown  through  the  cylinder  than  when  it  was  compelled 
to  drive  the  piston  against  external  pressure.  He 
accordingly  concluded  that  some  relation  must  exist 
between  the  quantity  of  heat  lost  by  the  steam  in  the 
cylinder  and  the  amount  of  work  done  in  the  same 
time  by  the  expansion  of  the  steam. 

The  results  of  his  reasoning  on  the  question  were 
summed  up  in  some  notes  made  by  him  but  not  pub- 
lished until  after  his  death.  He  says,  "Heat  is  simply 
motive  power,  or  rather  motion  which  has  changed 
form.  It  is  a  movement  among  the  particles  of  bodies. 
Whenever  there  is  a  destruction  of  motive  power,  there 
is  at  the  same  time  production  of  heat  in  quantity  exactly 
proportional  to  the  quantity  of  motive  power  destroyed. 
Reciprocally,  whenever  there  is  destruction  of  heat  there 
is  production  of  motive  power. 

' '  We  can  then  establish  the  general  proposition  that 
motive  power  is  in  quantity  invariable  in  nature — that 
it  is,  correctly  speaking,  never  either  produced  or 
destroyed.  It  is  true  that  it  changes  form — that  is,  it 
produces  sometimes  one  sort  of  motion,  sometimes  another, 
but  it  is  never  annihilated. ' ' 

Joule's  Determination. — Carnot  never  succeeded  in 
proving  experimentally  the  relation  between  heat  and 
what  he  called  motive  power,  or  the  power  to  do  work. 
This  experimental  proof  was  finally  given  by  Dr.  J.  P. 
Joule,  of  Manchester,  England.  Dr.  Joule  began  his 
experimental  investigation  of  the  subject  in  1840,  and 
worked  at  the  problem  for  ten  years  before  publishing 
his  final  conclusions.  He  found  that  a  given  quantity 
of  work  measured  in  foot-pounds  could  always  be  made 
to  produce  the  same  quantity  of  heat,  and  he  concluded 
as  the  result  of  all  of  his  experiments  that  773.64  foot- 


HEAT  143 

pounds  of  work  when  changed  into  heat  would  raise  the 
temperature  one  pound  of  water  by  one  degree  Fahren- 
heit. 

The  Conservation  of  Energy. — In  most  of  Joule's 
experiments  the  work  was  performed  by  weights 
actually  falling  under  the  influence  of  gravitation  and 
by  their  energy  turning  paddle-wheels  in  water  or 
rubbing  together  iron  plates  in  water  or  mercury.  The 
energy  of  the  falling  weight  was  thus  transformed  into 
heat  by  means  of  friction.  Many  experimenters  have 
since  worked  upon  the  same  problem  and  have  found 
that  the  same  amount  of  heat  is  produced  whether  the 
energy  is  transformed  by  means  of  friction,  percussion, 
the  electric  current,  or  any  other  process.  Carnot's 
conclusion  has  accordingly  been  experimentally  estab- 
lished, and  it  is  now  believed  that  the  total  energy  of 
the  physical  universe  is  a  quantity  which  can  neither 
be  increased  nor  diminished  by  any  known  process. 
This  theory  is  called  the  doctrine  of  the  Conservation 
of  Energy.  Heat  is  only  one  of  the  forms  in  which 
energy  may  be  manifested.  We  shall  see  later  that 
other  forms  of  energy,  as  the  electric  current,  the 
potential  energy  of  electric  charges,  and  the  energy  of 
Ether  vibrations  may  all  be  transformed  into  heat  or 
mechanical  energy  and  their  quantities,  like  the  calorie, * 
have  their  definite  mechanical  equivalents. 

The  Mechanical  Theory  of  Heat. — To  understand 
how  the  energy  of  a  moving  body  may  be  changed  into 
heat  it  will  be  necessary  to  recall  some  of  the  principles 
of  the  kinetic  gas  theory.  In  our  discussion  of  the 
relation  of  gas  pressure  to  molecular  velocities  (page 
95),  we  saw  that  according  to  our  theory  the  pressure 

*  For  definition  of  the  calorie  see  page  183. 


144  PHYSICS 

of  a  gas  confined  to  a  constant  volume  must  increase 
as  the  square  of  the  average  velocity  of  its  molecules 
increases.  We  express  this  mathematically  by  saying 
that  when  the  volume  is  constant  the  pressure  varies 
as  the  square  of  the  molecular  velocity,  or  p  oc  v2. 
The  product  pv  must  also  vary  as  v*,  and  since  an 
increase  of  v  means  a  corresponding  decrease  of  /, 
this  will  be  true  whether  the  volume  is  constant  or 
not;  hence,  we  may  write  as  before  pv  oc  ?A 

The  kinetic  energy  of  a  moving  molecule  also  varies 
as  the  square  of  its  velocity,  and  the  average  kinetic 
energy  of  all  the  molecules  in  the  gas  varies  as  the 
square  of  their  average  velocity,  hence  we  may  write 
E  oc  z/2,  where  E  represents  the  average  kinetic  energy 
of  the  gas  molecules. 

Since  pv  oc  v2  and  E  cc  z/2,  pv  oc  E. 

The  temperature  of  a  gas  measured  on  the  absolute 
scale  varies  as  the  volume  when  the  pressure  is  con- 
stant, or  varies  as  the  pressure  when  the  volume  is 
constant;  hence  T  oc  pv. 

We  can  accordingly  write  T  oc  £,  which  means  that 
the  temperature  of  a  gas  measured  on  the  absolute 
scale  (see  page  81)  varies  as  the  average  kinetic  energy 
of  its  molecules  varies. 

We  have  already  seen  that  work  done  upon  a  body 
may  increase  either  its  kinetic  energy  or  its  potential 
energy.  In  the  case  of  a  gas,  any  increase  of  molecu- 
lar kinetic  energy  will  increase  the  temperature  of  the 
gas.  That  which  we  call  heat  is,  in  a  gas,  only  the 
kinetic  energy  of  its  moving  molecules.  When  these 
molecules  strike  upon  the  skin  to  which  the  tempera- 
ture nerves  are  distributed  they  produce  the  sensation 
of  warmth.  When  they  strike  upon  the  walls  of  their 


HEAT  145 

containing  vessels  they  give  a  part  of  their  kinetic 
energy  to  the  molecules  of  the  walls,  and  the  tempera- 
ture of  the  gas  molecules  is  lowered  while  the  tempera- 
ture of  the  molecules  of  the  solid  is  raised. 

We  have  seen  that  the  average  distance  between  the 
molecules  of  a  gas  is  so  great  that  they  rebound  from 
each  impact  to  a  distance  greater  than  that  through 
which  cohesion  can  act,  so  that  although  two  molecules 
are  having  their  velocities  accelerated  while  approach- 
ing each  other  and  retarded  while  receding  from  each 
other,  their  total  potential  energy  is  neither  increased 
nor  diminished  by  the  number  of  their  collisions.  Since 
their  average  distance  is  already  greater  than  the  dis- 
tance through  which  cohesion  can  act,  an  increase  in 
the  volume  of  the  gas,  will  not  increase  their  potential 
energy.  In  the  case  of  a  liquid  the  conditions  are 
different.  Any  expansion  of  the  liquid  is  opposed  by 
cohesion,  and  hence  work  must  be  done  upon  the 
molecules  to  separate  them. 

Since  liquids,  as  well  as  gases,  expand  on  heating, 
any  increase  of  the  kinetic  energy  of  their  molecules  is 
accompanied  by  an  increase  of  volume.  Any  increase 
of  volume  of  the  liquid  means  that  the  average  distance 
between  its  molecules  is  increased.  This  gives  the 
molecules  more  potential  energy  than  they  had  before 
and  consequently  requires  the  expenditure  of  kinetic 
energy,  just  as  it  requires  the  expenditure  of  kinetic 
energy  to  lift  a  heavy  body  against  gravitation.  Con- 
sequently if  the  same  quantity  of  heat  could  be  given 
to  equal  masses  of  any  substance  in  the  liquid  and  in 
the  gaseous  form,  all  the  heat  given  to  the  gas  would 
increase  the  kinetic  energy  of  its  molecules  and  accord- 
ingly increase  its  temperature;  part  of  the  heat  given  to 


i46  PHYSICS 

the  liquid  would  increase  the  potential  energy  of  its 
molecules,  and  the  other  part  would  raise  its  tempera- 
ture. It  requires  about  twice  as  much  heat  to  raise  the 
temperature  of  a  gram  of  water  one  degree  as  it  does  to 
raise  the  temperature  of  a  gram  of  steam  one  degree. 
Accordingly,  about  half  the  heat  given  to  water  is  used 
up  in  increasing  the  potential  energy  of  its  molecules 
and  the  other  half  in  increasing  their  kinetic  energy. 

EFFECTS    OF    HEAT 

Expansion. — We  are  now  prepared  to  consider  in- 
telligently some  of  the  effects  of  heat  in  material 
bodies.  We  have  already  learned  of  its  expansion 
effects  in  gases,  and  have  seen  how  the  change  in 
gaseous  volume  or  pressure  may  be  used  as  a  measure 
of  the  temperature  change  in  the  gas. 

Liquids  and  solids  also  expand  when  heated,  but 
their  expansion  is  less  than  that  of  gases. 

Heat  Expansion  of  Water. 

LABORATORY  EXERCISE  48. — Place  the  overflow  vessel  used 
in  Laboratory  Exercise  40  on  one  pan  of  the  platform 
balance  and  fill  with  cold  water  (ice  water  preferred),  until 
some  of  the  water  overflows  into  a  vessel  placed  beside  the 
balance.  Balance  with  weights  on  the  other  pan,  and  as 
soon  as  your  balance  is  in  equilibrium  carefully  take  the 
temperature  of  the  water  with  a  thermometer.  Record  the 
weight  of  the  water  and  its  temperature.  Empty  the  vessel 
and  place  it  again  upon  the  balance  pan  and  pour  it  full  of 
boiling  water  until  some  overflows.  Record  the  weight  and 
temperature  as  before. 

Which  expands  more  rapidly  for  a  change  of  temperature, 
the  water  or  the  material  of  the  overflow  vessel  ?  (N.B.  If 
the  vessel  had  been  filled  by  a  solid  cylinder  of  its  own 
material,  the  cylinder  would  have  expanded  just  as  fast  as 
the  outside  vessel.  For  any  solid  cylinder  may  be  conceived 
as  made  up  of  concentric  cylinders  of  the  thickness  of  the 
outside  vessel,  and  if  these  did  not  expand  and  contract 


HEAT  147 

together  for  a  change  of  temperature,  the  outer  layers  would 
either  separate  from  the  inner  ones  or  would  be  broken  by 
the  greater  expansion  of  the  inner  ones.) 

From  the  known  weight  of  your  overflow  vessel,  calculate 
how  many  grams  of  water  it  held  at  each  of  the  measured 
temperatures.  Supposing  one  cubic  centimeter  of  the  cold 
water  used  in  your  experiment  to  weigh  one  gram,  what  was 
the  capacity  in  cubic  centimeters  of  your  overflow  vessel  at 
this  temperature  ? 

Your  vessel  being  made  of  tinned  iron,  its  expansion  is 
the  same  as  the  cubical  expansion  of  iron.  The  coefficient 
of  cubical  expansion  of  iron  is  .000036,  that  is,  the  volume 
of  iron  is  increased  by  .000036  of  itself  for  a  change  of  tem- 
perature of  one  degree  Centigrade.  What  was  the  capacity 
of  your  vessel  at  the  higher  temperature  measured  ? 

What  is  the  weight  of  one  cubic  centimeter  of  water  at 
this  temperature  ? 

What  is  the  volume  of  one  gram  of  water  at  this  tempera- 
ture ? 

What  is  the  mean  coefficient  of  cubical  expansion  of  water 
between  the  temperatures  measured  by  you  ?  (The  coefficient 
of  expansion  of  water  is  very  different  at  different  temperatures. 
Thus  between  nine  and  ten  degrees  Centigrade  it  is  .000077, 
while  between  eighty-nine  and  ninety  degrees  it  is  .00067.) 

If  a  glass  flask  whose  coefficient  of  cubical  expansion  is 
.000025  hold  1000  grams  of  water  at  the  temperature  of  the 
cold  water  used  in  your  experiment,  how  many  grams  of  the 
hot  water  of  your  experiment  will  it  hold  ? 

If  a  glass  bulb  having  the  same  expansion  coefficient  as 
the  flask  above  mentioned  weigh  250  grams  in  air  and  150 
grams  in  the  cold  water  of  your  experiment,  what  will  it 
weigh  in  the  hot  water  ? 

Linear. Expansion  of  Solids. 

LABORATORY  EXERCISE  49.* — Provide  a  piece  of  metal 
tubing  of  small  bore  and  about  one  and  a  half  meters  long. 
The  smallest  size  of  gas-pipe  will  answer  very  well  for  the 
experiment.  File  a  small  notch  in  one  side  about  twenty 
centimeters  from  the  end,  and  make  a  scratch  on  the  same 
side  exactly  one  meter  from  the  notch. 

*  The  different  forms  of  linear-expansion  apparatus  which  can  be  pur- 
chased of  dealers  answer  for  this  experiment. 


i48 


PHYSICS 


Place  two  blocks  or  other  supports  about  twenty  centi- 
meters high  upon  the  table,  upon  one  of  which  a  flat  strip 
of  iron  has  been  nailed  and  filed  to  a  knife-edge  to  fit  into 


FIG.  45. 

the  notch  in  the  tube.  Upon  the  other  support,  at  a  distance 
of  one  meter  from  the  knife-edge,  a  flat  piece  of  glass  should 
be  fastened  in  a  horizontal  position  with  tacks.  Cut  off  a 
piece  of  glass  tubing  two  or  three  millimeters  in  diameter 
and  four  or  five  centimeters  long,  and,  by  means  of  sealing 
wax  or  shellac,  fasten  a  long  pointer,  made  of  a  straw  or  a 
glass  thread  which  has  been  drawn  out  in  a  flame,  to  one 
end  of  the  glass  tube  at  right  angles  to  the  tube  and  about 
two  centimeters  from  the  larger  end  of  the  pointer.  Cut  the 
longer  arm  of  the  pointer  so  that  its  length  from  the  surface 
of  the  glass  tube  will  be  some  even  number  of  times  the 
diameter  of  the  tube.  Fifty  times  this  diameter  will  be  a 
convenient  length.  Stick  a  shot  or  a  bit  of  wire  to  the  short 
end  of  the  pointer  so  that  it  will  just  balance  the  long  end 
when  the  pointer  is  horizontal. 

Place  the  metal  tube  upon  the  supports,  letting  the  notch 
rest  upon  the  knife-edge,  and  place  the  glass  tube  with  the 
pointer  attached  upon  the  glass  plate  of  the  other  support, 
and  directly  under  the  scratch  on  the  metal  tube.  With  a 
radius  the  length  of  the  pointer  from  the  surface  of  the  glass 
tube  draw  an  arc  on  a  piece  of  cardboard  or  paper,  and 
with  a  pair  of  dividers  mark  it  off  into  a  scale  of  millimeters. 
Attach  this  scale  to  the  support  so  that  the  end  of  the 
pointer  will  just  reach  it,  and  so  that  the  center  of  the  arc 
is  at  the  point  where  the  glass  tube  rests  upon  the  glass. 

Connect  one  end  of  the  metal  tube  by  a  piece  of  rubber 
tubing  to  a  vessel  in  which  water  may  be  boiled.  (A  small 


HEAT  149 

tin  kerosene  can  may  be  used  for  a  boiler.  The  top  may 
be  screwed  down  tightly,  and  the  rubber  tubing  may  be 
attached  to  the  spout.* 

Adjust  the  pointer  so  that  it  rests  upon  one  division  of 
the  scale,  and  take  the  temperature  of  the  metal  tube,  which 
should  be  the  same  as  the  temperature  of  the  air  in  the  room 
if  the  tube  has  not  been  recently  handled.  Boil  the  water 
in  the  attached  vessel,  and  pass  the  steam  through  the  metal 
tube  and  out  through  a  piece  of  rubber  tubing  attached  to 
the  free  end  of  the  tube. 

As  the  tube  expands  the  pointer  moves  over  the  scale. 
When  the  expansion  has  ceased,  read  the  position  of  the 
pointer,  and  calculate  the  amount  of  expansion  of  one  meter 
of  the  tube.  Observe  that  the  glass  tube  and  pointer  form 
a  lever,  one  of  whose  arms  is  the  diameter  of  the  tube  and 
the  other  the  length  of  the  pointer. 

Assuming  the  final  temperature  of  the  metal  tube  as 
100°  C.,  calculate  the  expansion  of  the  tube  in  millimeters 
for  one  degree  of  temperature.  By  what  fraction  of  its 
length  does  the  tube  expand  for  a  change  of  temperature  of 
one  degree  ?  This  fraction  is  the  expansion  coefficient  of 
the  tube. 

Calling  /  the  length  of  your  tube  before  expansion,  /'  its 
length  after  expansion,  a  the  expansion  coefficient,  and  /  the 
temperature  change,  show  that  /'  =  /(i  -j-  at). 

The  expansion  coefficient  of  steel  is  about  .000012;  what 
space  should  be  left  between  the  ends  of  steel  rails  30  feet 
long  in  a  climate  where  the  temperature  change  may  amount 
to  40°  C.  ? 

Relation  between  Linear  and  Cubical  Expansion. 

—If  we  apply  our  equation  to  a   cube  the  length  of 
whose  edge  is  /,  we  know  that  after  heating  the  length 
of  its  edge  will  have  changed  from  /  to  /(i  -j-  at)  = 
(I  -f-  /  at)  and  its  volume  will  have  changed  from  /3  to 
(/+  I  at)*.     Cubing  (/+/#/),  and  omitting  all  of  the 


*  The  boiler  described  as  No.  80  in  the  list  of  apparatus  published  in 
the  Harvard  list  of  "Elementary  Exercises  in  Physics"  can  be  advan- 
tageously substituted  for  the  tin  can  in  this  exercise  and  in  Laboratory 
Exercise  57. 


PHYSICS 


quantities  which  are  multiplied  by  the  square  or  the 
cube  of  a  (a  is  never  so  great  as  .0001,  and  any 
ordinary  number  multiplied  by  a*  or  a3  becomes  very 
small),  we  have  lor  the  new  volume  (/3  -j-  3/3  at)  or 
/3(i  +  $at).  In  this  equation  3^  is  the  coefficient  of 
cubical  expansion  which  in  our  equation  for  gaseous 
expansion  on  page  81  we  have  expressed  by  b.  Hence 
if  b  is  the  coefficient  of  cubical  expansion  and  a  the 
coefficient  of  linear  expansion,  we  may  without  sensible 
error  write  b  =  3 a. 
Coefficients  of  Linear  Expansion. 


Expansion 
Coefficient. 


i  meter  heated  through 
50°  C.  expands 


Aluminum 000023 

Brass 19 

Copper 17 

Ebonite 80 

Glass 08 

Iron 12 

Lead 30 

Magnesium 26 

Nickel 13 

Platinum 09 

Silver 19 

Tin , 23 

Zinc 29 

Wood,  lengthwise — Oak 06 

Mahogany 04 

Fir 035 

Coefficients  of  Cubical  Expansion, 

Alcohol ooio  Mercury , 

Ether •. . . .  15  Petroleum. 

Ice ,..  012 


1.16  mm. 

•95 

.85 
4.00 

.40 

.60 
1.50 
1.30 

.65 

•45 

•95 


1-45 
•30 

.20 
•17 


.OOOlS 
90 


PROBLEMS. — Why  are  platinum  wires  used  for  sealing  into 
glass  ? 

Why  is  wood  better  than  metal  for  the  pendulum  rod  of 
a  clock  ? 


HEAT  151 

How  long  must  an  iron  bar  be  taken  in  order  that  its 
expansion  for  an  increase  of  temperature  may  equal  that  of 
a  bar  of  brass  one  meter  long  ? 

What  is  the  volume  at  300°  C.  of  a  piece  of  iron  having 
a  volume  of  i  cubic  centimeter  at  o°  ? 

If  a  piece  of  zinc  have  a  density  of  7  at  o°,  what  is  its 
density  at  100°  ? 

CHANGE   OF   STATE 

Melting. — We  are  all  familiar  with  the  phenomena 
of  the  change  of  bodies  from  the  solid  to  the  liquid  and 
from  the  liquid  to  the  gaseous  forms  when  their  tem- 
peratures are  sufficiently  increased. 

The  change  from  the  solid  to  the  liquid  state  by 
heating  is  called  Melting  or  Fusion. 

Conditions  of  Equilibrium  of  a  Solid  and  its  Liquid. 
— In  Laboratory  Exercise  44  we  saw  that  sulphur  may 
change  directly  from  the  solid  to  the  liquid  or  from  the 
liquid  to  the  solid  state  without  passing  through  any 
intermediate  condition,  while  sealing  wax  softens  or 
hardens  gradually. 

All  crystalline  substances  which  liquefy  on  heating 
change,  like  sulphur,  from  the  solid  to  the  liquid  state 
without  passing  through  any  intermediate  condition. 
In  such  cases  the  liquid  and  the  unmelted  solid  are  at 
the  same  temperature.  Any  increase  of  heat  changes 
some  of  the  solid  into  the  liquid  form  without  increas- 
ing its  temperature,  and  any  loss  of  heat  causes  some 
of  the  liquid  to  go  into  the  solid  form.  The  liquid  and 
the  unmelted  solid  may  accordingly  remain  in  contact 
with  each  other  without  changing  the  relative  quantity 
of  either  so  long  as  the  mass  neither  receives  nor  gives 
off  heat. 

Melting  Points.  — The  temperature  at  which  a  solid 
and  its  melted  liquid  may  remain  in  equilibrium  with 


1 52  PHYSICS 

each  other  is  called  the  Melting  Point  or  Fusion  Point 
of  the  substance.  Amorphous  substances,  like  sealing 
wax  or  glass,  which  change  gradually  from  the  solid! 
to  the  liquid  state,  cannot  be  said  to  have  any  definite 
melting  point. 

Disappearance  of  Heat  during  Fusion. — Since  the 
temperature  of  fusion  of  a  crystalline  substance  remains 
constant  until  all  the  substance  is  melted,  a  large 
amount  of  heat  may  often  be  given  to  the  substance 
without  increasing  its  temperature.  Before  the  relation 
between  heat  and  energy  was  understood,  this  loss  of 
heat  could  not  be  explained.  The  heat  was  supposed 
to  still  exist  in  the  liquid  in  some  form  incapable  of 
measurement,  and  was  accordingly  called  Latent  Heat. 
We  now  know  that  the  molecules  of  a  liquid  have  more 
potential  energy  of  cohesion  than  the  molecules  of  a 
solid,  and  that  to  give  them  this  potential  energy 
requires  the  expenditure  of  an  equal  quantity  of  kinetic 
energy.  In  the  solid  state  the  molecules  are  in  their 
condition  of  most  stable  equilibrium,  which  means  that 
their  potential  energy  is  less  than  in  any  other  condi- 
tion. Apparently  they  are  held  in  definite  positions 
with  relation  to  each  other  and  can  only  vibrate  back 
and  forth  within  certain  limits.  It  is  as  if  they  were 
held  together  by  attractions  between  definite  points  on 
the  molecules,  as  magnets  are  held  together  by  attrac- 
tions between  their  poles.  If  two  magnets  are  sep- 
arated, keeping  their  attracting  poles  turned  toward 
each  other,  work  must  be  done  upon  them,  and  they 
must  acquire  potential  energy.  If  instead  of  separating 
them  they  are  rotated  rapidly  about  axes  perpendicular 
to  the  line  joining  them,  their  attraction  for  each  other 
is  also  lessened  arid  their  potential  energy  increased, 


HEAT  153 

for  they  are  capable  of  doing  work  for  the  sake  of 
getting  back  to  their  positions  of  rest.  If  the  cohesion 
between  molecules  tends  to  bring  the  molecules  to  rest 
in  definite  positions  relative  to  each  other,  then  the 
potential  energy  between  molecules  may  be  increased 
by  separating  them,  or  by  setting  them  in  rapid  rota- 
tion. In  heating  a  body,  some  of  the  energy  given  to 
the  body  increases  the  energy  of  vibration  of  the  mole- 
cules, and  this  can  be  observed  in  the  expansion  of  the 
body  and  can  accordingly  be  measured  as  temperature. 
Another  part  may  increase  the  potential  energy  of  the 
molecules  by  increasing  their  average  distances  from 
each  other  or  by  setting  them  in  rotation.  When  a 
molecule  escapes  from  a  crystal  surface  into  the  liquid 
surrounding  it,  it  acquires  potential  energy  in  one  of 
these  forms  without  acquiring  any  additional  kinetic 
energy.  Hence  some  of  the  heat  used  in  melting 
bodies  disappears  as  molecular  kinetic  energy  and 
becomes  molecular  potential  energy.  In  changing 
back  from  the  liquid  to  the  solid  state,  the  potential 
energy  of  liquefaction  again  becomes  kinetic,  and  must 
be  given  off  to  surrounding  bodies  if  the  process  of 
solidification  is  to  continue.  Thus  the  freezing  of  one 
substance  must  result  in  the  warming  of  some  other 
substance.  In  our  experiments  on  heat  measurements 
we  shall  learn  how  to  measure  the  quantity  of  heat 
made  "  latent  "  in  the  process  of  fusion. 

Change  of  Volume  in  Melting. — Bodies  which  have 
a  definite  melting  point  usually  show  an  abrupt  change 
of  volume  on  liquefaction.  Most  substances  expand 
on  melting,  but  there  are  many  exceptions.  Solid 
substances  which  float  in  their  liquid  at  the  melting 
point  contract  on  melting.  Ice  is  the  most  notable 


iS4  PHYSICS 

example  of  this  kind.  Its  volume  contracts  by  nearly 
nine  per  cent  of  itself  on  melting.  This  fact  is  of  great 
importance  in  the  economy  of  nature.  The  ice  which 
forms  on  streams  and  lakes  in  the  winter  covers  the 
surface  of  the  water  and  prevents  the  rapid  loss  of  heat. 
If  it  settled  to  the  bottom,  the  water  in  the  colder 
regions  of  the  earth  would  be  entirely  frozen  in  the 
winter. 

Bismuth  contracts  about  2.3  per  cent  of  its  volume 
on  melting,  and  the  other  common  metals  expand. 
Metals  which  expand  on  melting  and  contract  on  cool- 
ing are  not  well  adapted  for  casting,  as  they  do  not 
take  sharp  impressions  of  the  mold.  Iron  contracts 
only  about  one  per  cent  on  solidification.  Copper  con- 
tracts about  seven  per  cent,  and  silver  more  than  eleven 
per  cent.  These  metals  are  accordingly  not  cast  into 
coins,  but  the  coins  are  stamped  out  of  the  solid  metal. 

Influence  of  Pressure  upon  the  Melting  Point. — 
Since  the  cohesion  attraction  is  so  great  between  the 
molecules  of  solids  and  liquids,  any  change  in  external 
pressure  affects  but  slightly  the  melting  point  of  solids. 
In  general,  substances  which  contract  on  melting  have 
their  melting  point  lowered  by  an  increase  of  pressure, 
and  substances  which  expand  on  melting  have  their 
melting  point  raised  by  an  increase  of  pressure.  The 
melting  point  of  ice  is  lowered  about  .0075°  C.  for  an 
increase  of  pressure  of  one  atmosphere,  or  about  one 
degree  for  a  pressure  of  a  ton  to  the  square  inch. 

When  ice  is  already  at  the  melting  point  it  may  be 
liquefied  by  pressure.  In  pressing  together  small  bits 
of  melting  ice  or  a  mass  of  snow  which  is  already  at  its 
melting  point,  the  pressure  may  become  great  enough 
at  the  points  of  contact  to  cause  some  of  the  solid  to 


HEAT  155 

melt,  and  thus  the  separate  particles  may  be  molded 
into  a  solid  mass.  In  this  case,  the  additional  poten- 
tial energy  required  by  the  liquid  particles  is  furnished 
by  the  work  done  in  compressing  the  mass. 

Energy  Changes  in  Solution. — When  a  solid  is 
changed  to  a  liquid  by  dissolving  it  in  another  liquid, 
a  quantity  of  kinetic  energy  is  changed  to  potential 
energy,  just  as  in  the  process  of  fusion,  and  the  tem- 
perature of  the  solution  is  lowered  by  the  loss  of  this 
kinetic  energy.  Frequently,  however,  a  contraction 
of  volume  takes  place  in  solution,  and  potential  energy 
is  lost  and  kinetic  energy  gained  by  this  contraction. 
This  gain  of  kinetic  energy  by  contraction  may  be 
greater  than  the  loss  of  kinetic  energy  by  the  liquefac- 
tion of  the  solid.  Thus  water  is  cooled  by  the  solution 
of  sodium  sulphate,  but  is  warmed  by  the  solution  of 
sodic  hydrate. 

Freezing  Mixtures. — In  some  cases  of  solution  the 
lowering  of  temperature  is  so  great  that  the  solution 
may  be  used  as  a  freezing  mixture.  Sometimes  two 
solids  when  mixed  will  combine  to  form  a  liquid  solu- 
tion, and  the  gain  in  potential  energy  of  both  sub- 
stances causes  a  great  decrease  in  their  kinetic  energy. 
Thus  two  parts  by  weight  of  ice  and  one  of  common 
salt  form  a  liquid  solution  which  has  a  freezing  point 
far  below  that  of  water.  In  the  preparation  ot  this 
solution  a  great  quantity  of  energy  is  changed  from  the 
kinetic  to  the  potential  form,  and  if  the  mixture  cannot 
acquire  heat  from  surrounding  bodies  its  temperature 
falls  as  much  as  twenty  degrees  below  zero  Centigrade. 
Such  a  mixture  of  salt  and  ice  is  frequently  used  as  a 
freezing  mixture. 

Vaporization. — The  change  from  the  solid  or  liquid 


i56  PHYSICS 

to  the  gaseous  state  is  known  as  vaporization.  Sub- 
stances which  vaporize  readily  are  said  to  be  volatile. 
We  have  already  seen  that  liquids  evaporate  at  ordinary 
temperatures,  and  that  a  certain  vapor  pressure,  which 
was  measured  in  Laboratory  Exercise  30,  is  necessary 
to  permanently  maintain  the  liquid  condition.  This 
process  of  vaporization  at  the  surface  of  a  liquid  we 
have  called  evaporation. 

In  Laboratory  Exercise  37  we  saw  that  the  vapor 
pressure  of  a  liquid  increases  as  the  temperature  of  the 
liquid  increases,  so  that  when  the  liquid  boils  its  vapor 
pressure  becomes  as  great  as  the  atmospheric  pressure. 

Boiling  Points. — The  temperature  at  which  the 
vapor  pressure  of  a  liquid  becomes  as  great  as  the 
atmospheric  pressure  upon  the  liquid  is  called  the  Boil- 
ing Point  of  the  liquid.  Since  the  vapor  pressure 
increases  with  the  temperature,  the  greater  the  atmos- 
pheric pressure  upon  the  surface  of  the  liquid  the  hotter 
must  the  liquid  be  at  its  boiling  point. 

The  vapor  pressures  of  many  liquids  at  different 
temperatures  have  been  determined  by  a  method  similar 
to  the  one  used  in  Laboratory  Exercise  30,  the  differ- 
ence being  that  the  top  of  the  Torricellian  tube  is  sur- 
rounded by  a  vessel,  which  can  be  filled  with  water  at 
any  temperature  desired,  and  the  vapor  pressure  of  the 
liquid  at  that  temperature  can  be  determined.  The 
vapor  pressure  of  water  at  zero  Centigrade  is  4.57 
millimeters  of  mercury,  or  more  than  6  grams  to  the 
square  centimeter,  and  water  will  accordingly  boil  at 
its  freezing  point  when  the  atmospheric  pressure  is 
reduced  to  this  amount. 

Lowering  of  Boiling  Point  by  Decrease  of  Pressure. 

LABORATORY    EXERCISE    50. — Select    a   round-bottomed 


HEAT 


'57 


Florence  flask  with  a  strong  neck,  fill  it  about  one  third  full 
of  water,  and  heat  it  over  a  flame  until  the  water  has  boiled 


FIG.  46. 

rapidly  for  some  time  to  drive  out  the  air  from  the  flask. 
Close  the  flask  with  an  air-tight  stopper  (a  rubber  stopper  is 
best  for  this  purpose),  and  support  it  neck  downwards 
upon  a  ring.  The  flask  will  then  contain  only  water  and 
water  vapor.  Place  the  neck  of  the  flask  in  water  so  that 
no  air  may  enter,  and  cool  the  flask  above  the  water  rapidly 
by  letting  cold  water  drip  upon  it.  This  will  condense  some 
of  the  water  vapor  upon  the  walls  of  the  flask,  and  will 
accordingly  lower  the  vapor  pressure  upon  the  contained 
water.  This  will  cause  the  water  to  boil.  Continue  in  this 
way  to  condense  the  vapor  and  to  cause  the  water  to  boil  as 
long  as  possible.  Then  withdraw  the  stopper  and  take  the 
temperature  of  the  water. 

The  accompanying  curve  shows  the  vapor  pressure 
of  water  in  centimeters  of  mercury  at  different  tempera- 
tures as  determined  by  Regnault.  Since  water  will 
boil  when  its  vapor  pressure  equals  the  external  gas 
pressure  upon  it,  this  curve  will  enable  you  to  deter- 


158 


PHYSICS 


mine  the  boiling  point  of  water  at  different  barometric 
pressures. 

PROBLEMS. — Taking  the  temperature  of  water  in  the  flask 
as  determined  in  the  preceding  experiment,  what  was  the 
lowest  vapor  pressure  which  you  were  able  to  produce  by 
cooling  the  flask  ? 

Water  within  the  receiver  of  an  air-pump  is  seen  to  boil 


VAPOR  PRESSURE  IN 

CENTIMETERS  OF  MERCURY. 
.*  10  o>  4^  01  05  via 
30  oooooc 

1 

/ 

) 

/ 

/ 

/ 

/ 

/ 

- 

- 

^--^ 

^ 

20       30       40       50       60       70       80 
TEMPERATURE  CENTIGRADE. 
FIG.  47. 

at  60°  C. ;  what  is  the  atmospheric  pressure  within  the 
receiver  ? 

At  what  temperature  will  water  boil  on  the  top  of  a 
mountain  where  the  barometer  stands  50  centimeters  high  ? 

What  is  the  barometric  height  on  a  mountain  where 
water  boils  at  90°  C.  ? 

It  will  be  seen  from  the  curve  that  the  vapor  pressure  does 
not  increase  uniformly  with  the  increase  of  temperature.  In 
the  neighborhood  of  100°  C.  this  increase  may  be  taken  as 
about  2.7  centimeters  for  a  change  of  temperature  of  one 
degree.  The  change  in  the  boiling  point  of  water  is  accord- 
ingly about  o°.  37  for  a  change  of  one  centimeter  in  the 
barometric  height. 


HEAT  159 

What  is  the  barometric  height  when  the  boiling  point  of 
water  is  99°.  26  ? 

Boiling  Points  of  Solutions. — When  a  substance 
dissolves  in  water  it  is  an  indication  that  the  cohesion 
between  its  molecules  and  the  water  molecules  is 
greater  than  between  the  molecules  of  water  or  the 
molecules  of  the  dissolved  substance.  Since  evapora- 
tion is  opposed  by  cohesion,  the  vapor  pressures  of  the 
substances  entering  into  the  solution  will  both  be 
lowered  by  the  solution.  If  the  dissolved  substance 
be  a  solid  or  a  liquid  having  a  lower  vapor  pressure 
than  water,  the  vapor  pressure  of  its  aqueous  solution 
will  be  lower  and  the  boiling  point  higher  than  for 
pure  water.  If  the  dissolved  substance  have  a  higher 
vapor  pressure  than  water,  the  vapor  pressure  of  the 
solution  will  be  less  than  that  of  the  more  volatile 
substance,  but  may  be  greater  or  less  than  that  of 
water. 

Distillation. — Two  volatile  liquids  in  solution  ac- 
cordingly each  have  their  own  vapor  pressure  in  the 
solution,  but  this  vapor  pressure  is  less  than  for  the 
substances  in  the  pure  state.  If  the  temperature  be 
sufficiently  raised,  one  of  the  liquids  will  boil  before 
the  other,  and  when  the  boiling  point  of  this  liquid  is 
reached  the  temperature  cannot  be  raised  until  some  of 
the  liquid  has  been  removed  by  boiling.  At  this  tem- 
perature, the  vapor  of  the  more  volatile  liquid  escapes 
more  rapidly  than  the  vapor  of  the  other  liquid,  and 
when  the  vapor  of  the  boiling  solution  is  again  con- 
densed into  a  liquid  it  will  contain  a  much  larger  per- 
centage of  the  more  volatile  constituent  than  did  the 
original  solution.  By  repeating  the  process,  a  still 
more  concentrated  solution  of  the  more  volatile  con- 


i6o 


PHYSICS 


stituent  can  be  prepared.      It  is  by  this  process  that 
alcohol  is  usually  separated  from  water. 

If  one  constituent  of  the  solution  have  a  very  low 
vapor  pressure,  the  other  constituent  may  be  almost 
completely  separated  from  it  by  boiling.  The  process 
of  separating  the  constituents  of  a  solution  by  boiling 


FIG.  48. 

off  the  more  volatile  one  and  condensing  it  again  in  a 
cold  vessel  is  known  as  Distillation.  When  both  of 
the  constituents  are  volatile  and  the  separation  is  only 
partial,  as  in  the  case  of  alcohol  and  water,  the  process 
is  known  as  fractional  distillation.  The  method  of  dis- 
tillation in  common  use  is  to  pass  the  vapor  from  the 
boiling  liquid  through  a  long  tube  cooled  in  water  and 
to  catch  the  condensed  liquid  in  another  vessel.  One 
arrangement  of  apparatus  commonly  used  in  the  labora- 


HEAT  161 

tory  is  shown  in  Fig.  48.  The  vessel  in  which  the 
liquid  is  boiled  is  called  the  still,  and  the  arrangement 
for  liquefying  the  vapor  is  called  the  condenser. 

Relation  of  Boiling  Point  of  Solution  to  Concentra- 
tion. 

LABORATORY  EXERCISE  51. — Weigh  out  about  10  grams  of 
common  salt  and  dissolve  in  about  100  cubic  centimeters  of 
water.  Boil  the  solution  in  a  beaker  or  flask  and  note  the 
temperature  of  the  boiling  point.  Let  the  boiling  continue 
until  the  water  is  mostly  boiled  off  and  salt  begins  to  pre- 
cipitate in  the  solution,  taking  the  temperature  of  the  boil- 
ing point  at  occasional  intervals.  When  there  is  not  sufficient 
water  left  to  dissolve  all  the  salt,  place  the  vessel  in  a  sand 
or  water  bath  and  let  the  evaporation  continue  until  the 
water  has  disappeared. 

Does  most  of  the  salt  remain  ?  How  does  the  increase  in 
the  concentration  of  the  solution  affect  its  boiling  point  ? 

Why  is  rain  water  fresh,  while  the  water  of  the  ocean  is 
salt  ? 

Which  will  boil  at  the  lower  temperature,  rain  water  or 
sea  water  ? 

Sublimation. — Some  solids  when  heated  pass  at 
once  from  the  solid  to  the  gaseous  state  without  passing 
through  any  intermediate  liquid  state.  This  process  is 
called  sublimation.  Thus,  if  a  crystal  of  iodine  be  put 
in  a  test  tube  or  a  glass  tube  sealed  at  one  end  and 
warmed  gently  over  a  flame,  the  iodine  will  at  once 
change  into  a  violet  vapor  which  will  condense  again 
into  crystals  on  the  cold  sides  of  the  tube. 

CONDENSATION    OF   ATMOSPHERIC   VAPOR 

Aqueous  Vapor  in  the  Atmosphere. — We  know  that 
water  is  constantly  evaporating  into  the  air,  and  that 
the  atmosphere  must  at  all  times  contain  considerable 
quantities  of  water  vapor.  We  have  also  seen  that  the 
quantity  of  water  vapor  which  can  exist  above  a  water 


162  PHYSICS 

surface  before  condensation  will  begin  depends  upon  the 
temperature.  The  curve  on  page  I  58  shows  the  maxi- 
mum vapor  pressure  which  can  exist  in  contact  with  a 
water  surface  at  different  temperatures.  Lowering  the 
temperature  or  decreasing  the  space  in  which  the  water 
vapor  is  confined  causes  some  of  it  to  condense  upon 
the  water  surface  or  upon  the  surface  of  the  containing 
vessel. 

Formation  of  Dew. — When  the  atmosphere  is  suffi- 
ciently cooled  its  vapor  will  likewise  condense  upon 
solid  or  liquid  surfaces  in  contact  with  the  air.  When 
atmospheric  vapor  condenses  upon  bodies  on  the  sur- 
face of  the  earth  it  is  called  Dew. 

The  Dew  Point.  —The  temperature  just  below  which 
dew  will  begin  to  condense  from  the  atmosphere  is 
called  the  Dew  Point.  When  the  temperature  of  the 
air  has  been  cooled  to  the  dew  point  the  air  is  said  to 
be  saturated  with  vapor,  and  the  dew  point  is  some- 
times called  the  temperature  of  saturation.  This  term 
is  misleading.  The  air  is  not,  and  cannot  become, 
saturated  with  vapor,  for  the  air  does  not  absorb 
moisture.  Evaporation  takes  place  into  the  air  just  as 
it  does  into  a  vacuum,  and  the  dew  point  is  not  affected 
by  the  presence  of  the  air.  When  the  surfaces  of 
bodies  exposed  to  the  water  vapor  in  the  air  are  suffi- 
ciently cooled,  the  water  molecules  which  strike  them 
lose  so  much  of  their  kinetic  energy  that  they  are  held 
to  the  surface  by  cohesion  instead  of  rebounding  from 
it  as  they  would  do  if  their  kinetic  energy  were  greater. 
When  these  same  surfaces  are  sufficiently  heated  the 
water  will  evaporate  from  them.  The  temperature  at 
which  as  much  water  is  condensed  upon  the  surface  as 
is  evaporated  from  it  in  the  same  time  is  the  tempera- 


HEAT 


163 


ture  of  the  dew  point.  Air  in  a  closed  receiver  con- 
taining water  is  always  at  its  dew  point  after  standing 
for  a  short  time. 

Determination  of  Dew  Point. 

LABORATORY  EXERCISE  52. — Fill  a  brightly  polished  metal 
vessel  (a  tin  cup  or  tin  can  will  do  as  well  as  anything) 
about  half  full  of  water  at  the  room  temperature.  Cool  this 
water  gradually  by  pouring  in  ice  water  from  another  vessel, 
stirring  the  water  all  the  time,  until  a  trace  of  moisture  can 
be  seen  on  the  outside  of  the  vessel.  Take  the  temperature 
of  the  water  with  a  thermometer.  Allow  the  vessel  of  water 
to  stand  and  become  warmer  until  the  moisture  disappears, 
and  take  the  temperature  again.  Add  a  little  cold  water 
and  note  again  the 
temperatures  at 
which  the  moisture 
appears  and  disap- 
pears, bringing 
these  two  tempera-  }JJ 
tures  as  c  1  o  s  e  1  y  g 
together  as  po  s-  g 
sible.  To  do  this, 
the  faintest  trace  of  ^ 
moisture  on  t  h  e  O 
vessel  must  be  ob-  < 
served.  This  can  > 
best  be  done  by  no- 
ting the  image  of 
some  object  re- 
fleeted  from  the 
brightly  polished 
surface.  Do  not  get 


10 
TEMPERATURE. 

FIG.  49. 


20 


near  enough  the  vessel  to  allow  your  breath  to  condense 
upon  it.  Take  the  mean  of  the  temperatures  of  appearance 
and  disappearance  of  the  moisture  as  the  dew  point. 

To  what  temperature  must  the  air  in  your  laboratory  fall 
before  dew  will  condense  upon  objects  in  the  room  ? 

The  curve  previously  referred  to  on  page  158  shows  the 
maximum  vapor  pressure  which  water  can  exert  at  different 
temperatures.  Since  this  maximum  pressure  is  exerted  when 


1 64  PHYSICS 

as  much  water  is  condensed  as  is  evaporated  in  the  same 
time,  which  is  the  condition  at  the  temperature  of  the  dew 
point,  the  curve  shows  the  temperature  of  the  dew  point  for 
any  vapor  pressure  given.  The  accompanying  curve,  Fig. 
49,  shows  this  same  pressure  in  millimeters  of  mercury  for 
temperatures  from  o°  to  20°  C. 

What  was  the  barometric  pressure  of  the  water  vapor  in 
the  air  at  the  time  of  your  experiment  ? 

What  part  of  the  observed  barometric  height  is  due  to  dry 
air,  and  what  part  to  water  vapor  ? 

What  is  the  dew  point  of  the  atmosphere  when  its  water 
vapor  exerts  a  barometric  pressure  of  10  millimeters  of 
mercury  ? 

The  Hygrometer. — Any  instrument  used  for  measur- 
ing the  quantity  of  aqueous  vapor  in  the  air  is  called  a 
Hygrometer.  The  instrument  by  means  of  which  you 
have  determined  the  dew  point  is  accordingly  a 
hygrometer. 

Formation  of  Frost. — When  the  water  vapor  of  the 
air  is  condensed  upon  a  surface  which  is  cooled  below 
the  freezing  point  of  water,  the  surface  becomes  covered 
with  a  coating  of  ice  crystals  called  hoar  frost.  This 
may  be  shown  by  allowing  the  moisture  to  condense 
upon  the  surface  of  "a  vessel  filled  with  a  freezing  mix- 
ture, as  broken  ice  and  salt.  The  crystalline  form  of 
ice  is  very  noticeable  in  hoar  frost,  especially  upon 
window  panes. 

Condensation  within  the  Atmosphere. — The  air  at 
all  times  contains  large  numbers  of  small  dust  particles 
which  have  been  carried  up  by  the  winds.  These 
particles,  though  too  small  to  be  seen  with  the  naked 
eye,  have  surfaces  upon  which  condensation  takes  place 
as  upon  larger  bodies.  Each  particle,  when  cooled 
below  the  dew  point  of  the  air,  becomes  covered  with 
condensed  moisture.  When  the  particles  with  their 


HEAT  165 

water  coating  become  large  enough  to  be  visible  to  the 
eye  they  form  a  fog  or  cloud.  If  the  moisture  con- 
tinues to  condense  upon  them,  they  soon  become  heavy 
enough  to  fall  rapidly,  and  are  then  called  rain  drops. 
Rain  is  accordingly  nothing  but  dew  which  has  con- 
densed upon  the  floating  particles  in  the  atmosphere. 
Air  can  be  artificially  freed  from  dust  particles  so  that 
no  fog  is  formed  in  it  when  it  is  cooled  far  below  its 
dew  point.* 

If  the  floating  particles  in  the  air  are  cooled  below 
the  freezing  point  of  water,  they  become  the  centers  of 
crystallization  for  the  ice  molecules  which  come  in  con- 
tact with  their  surfaces.  Snow  is  accordingly  hoar 
frost  deposited  upon  atmospheric  dust  particles. 

Formation  of  Clouds. — The  atmosphere  is  warmest 
near  the  surface  of  the  earth  and  cools  rapidly  as  it 
ascends.  When  it  is  cooled  below  its  dew  point  con- 
densation takes  place  upon  its  dust  particles  and  a 
cloud  is  formed.  If  the  water  drops  formed  upon  the 
dust  particles  are  small,  they  will  sink  toward  the  earth 
very  slowly.  When  they  have  settled  into  the  warmer 
air  below  them  the  water  evaporates  from  their  surfaces 
and  they  disappear.  The  bottom  of  a  cloud  accord- 
ingly represents  the  height  above  the  earth  at  which 
the  air  is  cooled  to  its  dew  point. 

When  the  air  near  the  earth's  surface  is  cooled  below 
its  dew  point,  the  clouds  settle  to  the  earth  and  we 
call  them  fog.  Since  the  air  very  near  the  earth  con- 
tains many  more  dust  particles  than  the  air  at  greater 
heights,  the  drops  of  water  formed  in  a  fog  are  usually 

*  Recent  experiments  have  shown  that  the  chemical  atoms  of  gases 
may  be  broken  up  into  parts  which  carry  electrical  charges,  and  that 
these  electrified  parts  of  atoms,  called  Electrons,  may  also  serve  as 
nuclei  for  the  condensation  of  the  water  vapor  of  the  atmosphere. 


1 66  PHYSICS 

more  numerous  than  in  a  cloud  In  cities  where  the 
air  is  filled  with  particles  of  dust  from  chimneys  and 
other  sources,  fogs  often  become  very  dense. 

PROBLEMS. — What  is  the  barometric  pressure  of  the  water 
vapor  in  the  air  on  a  foggy  day  when  the  temperature  is 
15°  C.? 

Water  vapor  is  about  .  6  as  heavy  as  air  at  the  same  pres- 
sure and  temperature;  calculate  the  weight  of  water  vapor  in 
your  laboratory  at  the  time  of  your  determination  of  the  dew 
point. 

CRITICAL  TEMPERATURES   AND   PRESSURES 

Critical  Temperatures. — We  have  seen  that  the 
vapor  pressure  of  water  rises  as  the  temperature  rises. 
At  1 00°  C.  it  is  equivalent  to  76  centimeters  of  mer- 
cury. At  200°  C.  it  is  equivalent  to  1169  centimeters 
of  mercury,  more  than  15  atmospheres.  At  a  tem- 
perature of  365°  C.  no  known  pressure  can  condense 
water  vapor  into  a  liquid.  When  heated  to  this  tem- 
perature in  a  closed  vessel  no  surface  of  separation  can 
be  observed  between  the  water  and  the  steam. 

The  temperature  at  which  the  whole  of  a  liquid 
changes  into  vapor  under  the  greatest  possible  pressure 
that  can  be  applied  to  it  is  called  the  Critical  Tem- 
perature of  the  liquid.  At  this  temperature  the  kinetic 
energy  of  the  molecules  becomes  so  great  that  they 
will  rebound  from  each  other  after  each  impact  not- 
withstanding the  cohesion  attraction.  The  critical 
temperature  of  water  is  accordingly  365°  C. 

Liquefaction  of  Gases.— When  a  liquid  is  heated 
above  its  critical  temperature  it  becomes  a  permanent 
gas,  and  cannot  be  liquefied  by  pressure.  The  gases 
of  the  atmosphere  are  at  all  times  above  their  critical 
temperature  and  cannot  be  liquefied  until  they  are 


HEAT 


167 


cooled  far  below  atmospheric  temperatures.  When 
their  temperatures  are  sufficiently  lowered,  all  gases 
may  be  liquefied  by  pressure. 

After  a  gas  has  been  liquefied  the  external  pressure 
may  be  reduced  and  the  liquefied  gas  will  boil  away  at 
a  constant  temperature  which  is  always  lower  than  its 
critical  temperature.  Thus  air  at  a  temperature  of 
—  140°  C.  and  under  a  pressure  of  39  atmospheres  is 
condensed  to  a  liquid  which  at  atmospheric  pressure 
will  boil  at  a  temperature  of  --  191°  C.  Hydrogen  at 
a  temperature  of  —  223°  C.  and  a  pressure  of  15 
atmospheres  is  condensed  to  a  liquid  which  boils  at 
-  238°. 5  C.,  and  which  freezes  to  a  solid  mass  at 
about  —  256°  C. 

Table  of  Critical  Constants  of  Gases. — The  follow- 
ing table  shows  the  critical  temperatures,  the  pressures 
necessary  to  liquefy  the  gases  at  these  temperatures 
(called  Critical  Pressures),  and  the  boiling  points  of  a 
few  of  the  common  gases. 


Gas. 

Crit.  Temperature. 

Crit. 
Pressure. 

Boiling  Point. 

C. 

Abs. 

C. 

Abs. 

Hydrogen  

-223» 
—  146° 
-II9° 
-  140° 

31° 

50° 
I27- 

154° 
133° 
304° 

15  at. 

35    " 
5i    " 
39    " 

73    " 

-  238°-5 
-  i94°-5 
-  i8ic.5 
-191° 

-      78°.2 

34°-5 
78°.5 
9i°-5 
82° 

i94°-8 

Nitrogen 

Oxygen  

Air  

Carbon  dioxide  

Lowest  Known  Temperature. — The  lowest  tempera- 
ture yet  reached  has  been  produced  by  allowing 
liquefied  hydrogen  to  boil  at  a  low  pressure,  about  35 
millimeters  of  mercury.  The  temperature  which  has 
been  reached  in  this  way  is  believed  to  be  as  low  as 


1 68  PHYSICS 

-  259°  C.,  or  only  14°  above  the  absolute  zero.  It  is 
by  means  of  the  low  temperature  produced  in  this  way 
that  liquid  hydrogen  may  be  frozen. 

ENERGY   CHANGES   IN   VAPORIZATION 

Disappearance  of  Heat  during  Vaporization. — We 

have  already  learned  that  the  molecules  of  any  sub- 
stance have  more  potential  energy  in  the  gaseous  than 
in  the  liquid  form.  It  must  accordingly  require  an 
expenditure  of  kinetic  energy  to  change  a  substance 
from  the  liquid  to  the  gaseous  form.  The  kinetic 
energy  thus  expended  is  known  as  the  Latent  Heat  of 
Vaporization. 

Cooling  of  Ether  by  Evaporation. 

LABORATORY  EXERCISE  53. — Provide  two  test  tubes,  one 
of  which  will  slide  easily  within  the  other.  Pour  a  little 
water  into  the  large  tube  and  push  the  smaller  one  down  into 
the  water  to  the  bottom  of  the  larger.  The  water  will  rise 
between  the  tubes  and  overflow,  and  the  space  between  them 
will  be  filled  with  water. 

Pour  the  inner  tube  about  half  full  of  ether,  taking  care 
that  none  gets  into  the  water  between  the  tubes.  Through 
a  glass  tube  reaching  nearly  to  the  bottom  of  the  ether  blow 
air  from  a  foot  bellows  or  the  lungs  so  that  it  will  rise  in 
large  bubbles  through  the  ether.  This  will  cause  rapid 
evaporation  of  the  ether,  and  some  of  the  heat  used  up  in 
increasing  the  potential  energy  of  the  ether  molecules  will 
be  taken  from  the  water  surrounding  the  tube.  If  the  outer 
tube  be  held  so  that  it  does  not  receive  heat  from  the  hand 
or  other  body,  the  water  between  the  tubes  may  be  frozen. 

The  experiment  may  be  modified  by  evaporating  ether 
rapidly  from  a  watch  crystal  set  upon  a  drop  of  water  on  a 
board. 

Drop  a  little  ether  on  the  hand  and  note  the  cooling 
sensation. 

Wrap  a  thin  cloth  about  a  thermometer  bulb  and  moisten 
it  with  ether  which  has  been  standing  in  the  room  until  its 


HEAT  169 

temperature  is  about  that  of  the  air  in  the  room.  What 
change  do  you  observe  in  the'  thermometer  ? 

Tie  a  thin  piece  of  cloth  about  a  thermometer  bulb,  and 
dip  one  end  of  it  in  water  at  the  room  temperature  and  let 
the  water  rise  by  capillarity  and  evaporate  from  around  the 
thermometer  bulb.  Note  any  temperature  change  that  may 
occur  in  the  thermometer. 

Would  the  water  evaporate  faster  on  dry  or  on  a  moist 
day  ?  Would  the  difference  in  temperature  between  a  wet- 
bulb  and  a  dry-bulb  thermometer  be  greater  on  a  dry  or  on 
a  moist  day  ? 

The  Psychrometer. — A  wet-  and  a  dry- bulb  ther- 
mometer mounted  side  by  side  form  an  instrument 
much  used  for  estimating  the  humidity  of  the  air.  This 
instrument  is  called  a  psychrometer.  It  is  impossible 
to  calculate  theoretically  the  humidity  of  the  air  from 
this  instrument,  but,  by  a  long  series  of  observations 
upon  it  in  connection  with  the  dew-point  determina- 
tions by  other  means,  hygrometer  tables  have  been 
made  which  give  very  approximately  the  amount  of 
aqueous  vapor  in  the  air  from  the  readings  of  this 
instrument. 

DISTRIBUTION   OF   HEAT 
CONDUCTION 

Definition. — Heat  is  conveyed  from  one  body  to 
another  in  several  different  ways.  When  heat  is  trans- 
ferred from  one  particle  to  another  through  a  body,  the 
process  is  called  conduction. 

Conduction  in  Solids. — Solids  differ  greatly  in  their 
capacities  for  conducting  heat.  Accurate  measurement 
of  the  amount  of  heat  carried  by  a  body  is  a  difficult 
process,  but  it  is  easy  to  show  qualitatively  that  one 
body  may  conduct  heat  better  than  another.  If  wires 


170  PHYSICS 

of  copper  and  iron  of  the  same  size  be  held  in  the  hand 
while  an  end  of  each  is  heated  red  hot  in  a  flame,  the 
copper  wire  will  feel  hot  at  a  greater  distance  from  the 
flame  than  the  iron  wire.  A  glass  rod  may  be  held  in 
the  fingers  very  close  to  the  flame  while  its  end  is 
melted.  A  lighted  match  may  be  held  until  the  flame 
has  burned  very  near  to  the  fingers  without  any  per- 
ceptible heating  of  the  wood. 

This  difference  in  the  heat  conductivity  of  bodies 
causes  them  to  seem  of  very  different  temperatures 
when  all  are  practically  at  the  temperature  of  the  sur- 
rounding air.  We  judge  of  the  temperature  of  bodies 
when  in  contact  with  our  skin  by  the  rate  at  which  heat 
is  gained  or  lost  by  the  skin.  A  very  cold  body  which 
is  a  poor  conductor  of  heat  may  feel  warmer  to  our 
touch  than  a  body  less  cold  which  is  a  better  conduc- 
tor of  heat.  In  the  former  the  surface  in  contact  with 
the  hand  is  very  soon  warmed,  while  in  the  latter  the 
heat  is  conducted  away  nearly  as  rapidly  as  it  is 
received. 

The  nature  of  heat  conduction  in  solids  is  not  at  all 
understood.  If  the  vibrating  molecules  actually  strike 
against  each  other  and  divide  their  energy  in  this  way, 
it  is  thought  that  conduction  should  be  a  more  rapid 
process  than  it  is.  Then  we  have  seen  reasons  for 
believing  that  in  crystalline  bodies,  at  least,  the  mole- 
cules are  spaced  at  definite  distances  from  each  other 
and  accordingly  should  not  strike  against  each  other 
in  their  vibrations.  In  this  case,  the  vibrations  of  one 
molecule  could  disturb  another  one  only  by  setting  up 
vibrations  in  s^me  medium  extending  between  them. 

Law  of  Conductivity. — The  quantity  of  heat  which 
will  pass  through  a  conductor,  say  a  metal  plate,  in  a 


HEAT  171 

given  time  is  proportional  to  the  difference  of  tempera- 
ture of  the  two  faces  of  the  conductor  and  to  the  area 
of  the  cross-section  of  the  conductor,  and  is  inversely 
proportional  to  the  thickness  of  the  plate. 

Thus  if  Q  represent  the  quantity  passing  through 
the  conductor,  T^  the  temperature  of  one  face,  T2  the 
temperature  of  the  other  face,  e  the  thickness  of  the 
plate,  and  A  the  area  of  its  cross-section, 

T  -     T 
Q=k    l   e     2A, 

where  k  is  a  constant  factor  for  the  given  material  but 
is  different  for  different  materials,  and  is  called  the 
coefficient  of  conductivity.  V/ 

Conduction  in  Liquids. — If  a  piece  of  ice  be  held  in 
the  bottom  of  a  test  tube  of  water  by  means  of  a  weight 
of  lead  or  a  piece  of  wire,  and  the  test  tube  be  inclined 
over  a  flame  so  that  it  is  heated  about  the  middle  of  the 
tube,  the  water  may  be  boiled  without  melting  the  ice 
below  it.  This  shows  that  water  is  a  very  poor  con- 
ductor of  heat.  The  same  may  be  said  of  all  liquids 
except  mercury. 

Conduction  in  Gases. — The  determination  of  the 
heat  conductivity  of  gases  is  a  matter  of  extreme  diffi- 
culty, as  it  is  impossible  to  tell  how  much  of  the  heat 
has  been  carried  by  conduction  proper,  as  in  solids, 
and  what  part  by  gas  currents.  A  hot  body  will  cool 
more  rapidly  in  hydrogen  than  in  air,  but  it  is  impossi- 
ble to  prevent  diffusion  currents  in  the  gases,  while 
such  currents  do  not  exist  in  true  conduction  in  solids. 

Table  of  Conductivities. — The  following  table  will 
give  the  conductivities  of  various  substances  as  referred 
to  the  conductivity  of  silver  taken  as  100: 


172 


PHYSICS 


Solids. 


Fluids. 


Silver 100 

Copper 73.6 

Gold 53.2 

Tin 15.2 

Iron 11.9 

Lead 8.5 

Brass 27.3 

German  silver 6.3 

Ice .21 

Glass 046 

Hard  rubber 024 


Mercury 1.35 

Water 140 

Glycerine 084 

Alcohol 052 

Ether 046 

Olive  oil 045 

Chloroform 041 

Air 0066 

Hydrogen 0468 

Carbon  dioxide 0039 

Illuminating  gas 0176 


Through  what  thickness  of  silver  will  heat  flow  as  rapidly 
as  through  i  millimeter  of  hard  rubber  ? 

On  account  of  its  low  conductivity,  a  layer  of  ice 
over  water  is  a  great  protection  from  further  freezing. 


CONVECTION 

Formation  of  Currents  by  Gravitation. — If  liquids 
and  gases  were  removed  from  the  action  of  gravitation, 
their  principal  method  of  heat  distribution  would  be  by 
means  of  diffusion.  The  effect  of  gravitation  is  to  set 
up  currents  in  the  heated  fluids  and  in  this  way  to 
greatly  hasten  the  diffusion  process. 

We  have  seen  that  fluids  are  expanded  by  heat,  and 
that  on  account  of  their  increase  in  volume  the  heated 
parts  have  their  density  decreased  and  are  pushed  up 
by  the  colder  parts.  A  liquid  or  a  gas  heated  at  the 
bottom  will  accordingly  have  ascending  and  descend- 
ing currents  set  up  in  it,  and  by  means  of  these  the 
cooler  parts  of  the  fluid  will  constantly  be  brought  into 
contact  with  the  source  of  heat. 

Thus  in  the  experiment  with  the  ice  and  the  boiling 
water  in  the  test  tube  it  is  necessary  to  heat  the  water 


HEAT 


above  the  ice,  as  otherwise  the  water  cannot  be  heated 
until  after  the  ice  is  melted.  The  same  conditions 
exist  in  the  air.  The  hand  held  above  a  heated  iron 
will  feel  the  heat  much  more  plainly  than  if  held  below 
it. 

The  ascending  and  descending  currents  set  up  by 
gravitation  in  a  heated  liquid  or  gas  are  called  Convec- 
tion Currents.  The  distribution  of  heat  by  means  of 
these  currents  is  called  Convection. 

Convection  Currents  in  Water. 

LABORATORY  EXERCISE  54. — Fill  a  small  beaker  with  clear 
water  and  allow  it  to  stand  protected  from  direct  sunlight 
until  the  water  has  come  to  rest,  say  for  five  minutes.  Dip 
a  pen  into  aniline  ink,  as  violet  or  green  ink,  and  touch  it 
to  the  surface  of  the  water,  leaving  colored  ink  on  the  sur- 
face. This  ink  will  diffuse  into  the  water  very  slowly,  but 
it  will  be  carried  about  by  any 
currents  in  the  water.  If  the 
water  is  colder  than  the  room, 
there  will  be  ascending  currents 
around  the  outside  of  the  vessel 
and  descending  currents  in  the 
center,  and  these  will  be  shown 
by  the  movements  of  the  colored 
water.  If  the  water  is  warmer 
than  the  air,  the  descending 
currents  will  be  around  the  out- 
side of  the  vessel.  If  one  side 
of  the  vessel  receive  more  heat 
than  the  side  opposite,  there 
will  be  ascending  currents  on 
the  warmer  side.  The  best 
currents  for  experimentation  are 
slender  ones,  such  as  are  shown 
in  Fig.  50.  If  these  do  not 
appear  on  first  trial,  repeat  with 
another  beaker  of  water. 

After  the  currents  are  plainly 
indicated  by  the  colored  ink  columns,  hold  the  warm  finger 


174  PHYSICS 

against  the  side  of  the  vessel  near  a  slender  descending  cur- 
rent and  explain  the  movement  produced  in  the  current. 
Do  the  same  near  an  ascending  current.  Light  a  match  and 
hold  against  one  side  of  the  beaker. 

Place  a  beaker  of  water  where  the  sun  shines  upon  one 
side  of  it,  and  after  it  has  stood  for  a  few  minutes  touch  the 
surface  with  the  ink  and  account  for  the  currents  produced. 

Fill  a  test  tube  with  cold  water  and  stand  it  inclined  at 
an  angle.  After  it  has  stood  for  a  few  minutes,  touch  the 
ink  to  the  water  and  explain  the  currents. 

Importance  of  Convection  Currents  in  Nature. — 
Convection  currents  play  a  very  important  part  in  the 
economy  of  nature.  The  atmospheric  and  oceanic  cir- 
culations are  entirely  carried  on  by  them.  With  the 
exception  of  the  tides,  all  the  energy  of  wind  or  ocean 
currents  is  derived  from  convection  currents. 

Heating  and  Ventilation  of  Houses. — In  warming 
and  ventilating  our  houses  we  make  frequent  use  of 
convection  currents.  We  remove  the  smoke  and  the 
gaseous  products  of  combustion  from  our  fires  by  build- 
ing chimneys  in  which  a  column  of  air  can  become 
heated  without  diffusing  into  the  surrounding  atmos- 
phere. This  column  of  air  expands  and  becomes 
lighter  than  a  column  of  the  surrounding  air  of  the 
same  height,  consequently  it  is  pushed  upward  by  the 
buoyant  force  of  the  colder  air.  The  taller  the  hot-air 
column,  the  more  difference  there  is  between  its  weight 
and  the  weight  of  a  column  of  the  surrounding  air  of 
the  same  height,  hence  the  greater  the  unbalanced 
upward  pressure  against  it,  and  the  greater  the  draught 
in  the  chimney. 

In  the  hot-air  furnace  used  for  warming  buildings, 
the  air  is  heated  in  a  chamber  above  the  fire.  Pipes 
lead  upward  from  this  chamber  to  the  rooms  where  the 
heat  is  wanted,  and  another  pipe  runs  downward  and 


HEAT  175 

outward  to  the  cold  air  outside  the  building.  The 
constant  pressure  exerted  by  the  cold  outside  air 
pushes  the  lighter  air  in  the  pipes  upward  into  the 
rooms  and  through  flues  or  other  openings  in  the  walls 
into  the  outside  air  again. 

In  the  warm -water  heaters  the  conditions  are  similar 
except  that  the  cold  water  is  taken  from  a  reservoir  in 
the  top  of  the  house,  from  which  it  flows  downward 
into  the  heating  apparatus  and  pushes  up  the  columns 
of  warm  water  which  go  through  the  radiators  in  the 
rooms  and  then  discharge  into  the  cold-water  reser- 
voir. The  warm-  and  cold-water  columns  are  of  the 
same  height,  and  since  the  water  is  continually  lighter 
in  one  column  than  in  the  other  equilibrium  is  im- 
possible. 

Questions  on  Convection. 

Why  can  you  not  produce  convection  currents  in  a  liquid 
by  heating  it  at  the  top  ? 

Why  is  it  easier  to  ventilate  a  room  by  means  of  two  small 
openings  than  by  one  large  one  ? 

If  a  door  between  a  warm  and  a  cold  room  stand  open  a 
few  inches  and  a  lighted  candle  be  moved  upward  and 
downward  in  front  of  the  opening,  the  flame  will  be  blown 
from  the  warm  room  toward  the  cold  room  at  the  top  of  the 
door,  and  from  the  cold  room  toward  the  warm  room  at  the 
bottom.  Why  ? 

If  a  lamp  chimney  be  set  over  a  burning  candle  so  that 
no  air  can  enter  at  the  bottom,  the  candle  will  go  out. 
Why? 

If  a  partition  made  by  a  little  piece  of  cardboard  be  put 
in  the  top  of  the  chimney,  the  candle  will  continue  to  burn. 
Explain. 

Why  will  a  match  burn  faster  when  the  lighted  end  is  held 
downward  than  when  it  is  held  upward  ? 


176  PHYSICS 

RADIATION 

Transference  of  Energy  through  a  Vacuum. — Heat 
may  be  transferred  from  a  warm  to  a  cold  body  in  a 
vacuum.  Here  the  process  can  be  neither  conduction 
nor  convection.  In  conduction  the  heat  is  passed  from 
one  particle  to  another  of  a  material  body,  while  in 
convection  the  heat  is  carried  by  the  movements  of 
heated  material  particles.  If  we  define  heat  as  on 
page  144  as  the  kinetic  energy  of  moving  molecules, 
then  there  can  be  no  heat  in  a  vacuum ;  nevertheless 
molecules  may  lose  their  kinetic  energy  in  a  vacuum, 
while  other  molecules  may  gain  kinetic  energy  from 
the  vacuum.  We  accordingly  conclude  that  what  we 
call  a  vacuum  is  filled  with  a  medium  which  is  not 
apparent  to  any  of  our  senses  but  which  is  capable  of 
transmitting  energy.  This  medium  is  known  as  the 
Luminiferous  Ether,  because  it  was  first  recognized  by 
the  part  which  it  takes  in  the  phenomenon  of  light. 
The  energy  absorbed  by  the  luminiferous  ether  is  sup- 
posed to  exist  in  some  form  of  vibration,  and  is  called 
Radiant  Energy. 

Definition  of  Radiation. — The  process  by  which 
radiant  energy  is  transmitted  in  the  Ether  is  called 
Radiation. 

Mutual  Transformation  of  Heat  and  Radiant 
Energy. — The  process  of  radiation  is  most  conven- 
iently studied  in  connection  with  the  subject  of  light. 
Some  of  the  conditions  under  which  heat  is  transformed 
into  radiant  energy  and  radiant  energy  into  heat  may 
be  noted  here. 

All  of  the  energy  received  from  the  sun  comes  to  us 
by  means  of  radiation.  When  this  energy  is  trans- 
formed into  heat  it  is  said  to  be  absorbed. 


HEAT  177 

Absorption  of  Radiant  Energy. 

LABORATORY  EXERCISE  55. — Place  a  piece  of  transparent 
glass  and  a  piece  of  smoked  glass  in  the  sunlight  with  their 
surfaces  inclined  at  the  same  angle  to  the  sun's  rays,  and 
decide  by  the  sense  of  touch  which  is  heated  the  more 
rapidly. 

Take  two  small  flasks  of  the  same  size,  smoke  the  outside 
of  one  over  a  candle  flame,  fill  both  with  cold  water  at  the 
same  temperature,  insert  thermometers  in  the  corks  of  both 
and  set  them  in  the  sunlight.  Which  absorbs  heat  the  more 
rapidly  ? 

Fill  them  both  with  hot  water  at  the  same  temperature 
and  set  them  in  the  shade.  Which  cools  the  more  rapidly  ? 

Selective  Absorption. — Substances  frequently  allow 
one  sort  of  radiant  energy  to  pass  through  them,  but 
absorb  radiant  energy  of  another  sort.  Thus  glass 
allows  the  radiant  energy  from  the  sun  to  pass  through 
it,  but  reflects  and  absorbs  the  radiant  energy  from  a 
hot  stove.  The  air  allows  the  radiant  energy  of  the 
sun  to  pass  through  it  with  little  loss,  but  absorbs  the 
radiant  energy  of  the  heated  earth.  This  is  especially 
true  of  the  water  vapor  in  the  air.  It  is  for  this  reason 
that  the  atmosphere  is  heated  at  the  bottom  instead  of 
at  the  top.  If  the  atmosphere  were  absent  from  the 
earth,  the  difference  between  night  and  day  temperature 
would  be  much  greater  than  it  is.  In  very  dry  regions 
where  the  air  contains  but  little  water  vapor  the  tem- 
perature extremes  are  much  greater  than  in  moist 
regions. 

Reflection  of  Radiant  Energy. 

LABORATORY  EXERCISE  56, — With  a  concave  mirror  reflect 
the  sunlight  upon  a  piece  of  paper.  Move  the  paper  until 
the  spot  of  light  reflected  from  the  mirror  is  as  small  as 
possible  and  note  if  there  is  any  heating  effect  upon  the 
paper.  Can  radiant  energy  be  reflected  ?  Does  radiant 
energy  pass  through  glass  ? 


1 78  PHYSICS 

Relation  between  Radiation  and  Absorption. —We 
have  seen  from  the  above  experiments  that  bodies 
differ  in  their  capacity  for  taking  up  radiant  energy  and 
for  giving  off  their  heat  energy  in  the  form  of  radiation. 
Apparently  if  the  molecules  of  a  body  are  easily  set  in 
vibration  by  the  Ether,  their  vibrations  are  likewise 
rapidly  damped  by  the  Ether,  so  that  bodies  which 
readily  absorb  radiant  energy  also  readily  lose  their 
own  heat  energy  by  radiation. 

HEAT   MEASUREMENTS 

Two  Kinds  of  Measurements. — Two  kinds  of  heat 
measurements  are  possible.  We  may  measure  the 
intensity  of  heat  in  a  body,  or  we  may  measure  the 
total  quantity  of  heat  energy  in  the  body.  The  former 
we  call  the  temperature  of  the  body,  and  the  latter  the 
heat  quantity  of  the  body. 

We  have  seen  that  temperature  is  the  measure  of  the 
average  kinetic  energy  of  the  molecules  of  a  body.  If 
a  body  consisting  of  only  a  few  molecules  contains  a 
large  quantity  of  heat  energy,  then  the  average  kinetic 
energy  of  its  molecules  must  be  great  and  its  tempera- 
ture is  high.  The  same  quantity  of  heat  given  to 
another  body  consisting  of  more  molecules  will  not 
raise  its  temperature  so  high. 

THERMOMETRY 

Definition. — The  measurement  of  temperature  is 
called  Thermometry.  Temperature  measurements  may 
be  based  upon  any  property  of  bodies  which  varies 
continuously  with  temperature  changes.  We  have  seen 
that  the  expansion  of  gases  is  such  a  property,  and  our 
absolute  scale  of  temperature  is  based  upon  gas  expan- 
sion. 


HEAT 


179 


Construction  of  Thermometers. — An  instrument  for 
measuring  temperature  changes  by  means  of  the 
expansion  of  bodies  is  called  a  thermometer.  The 
expanding  substance  used  is  generally  a  gas  or  a 
liquid,  and  must  be  enclosed  in  a  solid.  The  observed 
expansion  is  accordingly  the  difference  in  the  expan- 
sion of  the  fluid  and  of  its  containing  vessel. 
1,10 


1.09 
1.08 
1.07 
1.06 
1.05 
1,04 
1.03 
1.02 
1.01 


20       3-0 


40       50        60 
TEMPERATURE. 

FIG.  51. 


70       80       90     10e 


There  are  several  requisites  for  a  satisfactory  fluid  to 
be  used  in  a  thermometer.  The  substance  should  not 
change  its  properties  on  heating.  It  should  have  a 
large  and  uniform  expansion  coefficient  and  it  should 


i8o  PHYSICS 

be  a  good  conductor  of  heat.  The  curves  in  Fig.  51 
show  the  expansion  of  a  gas,  of  mercury,  and  of 
water.  From  these  it  will  be  seen  that  a  gas  (and 
from  what  we  know  of  gaseous  conductivity,  hydrogen 
gas)  most  nearly  meets  the  .equirements  for  a  perfect 
thermometer  fluid.  Hydrogen  thermometers  are  ac- 
cordingly used  as  standards,  but  on  account  of  the 
inconvenience  of  making  temperature  measurements 
with  them  they  are  replaced  in  practice  by  mercury 
thermometers. 

Graduation  of  Thermometers. — Thermometers  are 
regularly  graduated  by  determining  the  height  of  the 
mercury  column  at  two  fixed  temperatures,  and  by 
dividing  the  difference  in  these  heights  into  some  num- 
ber of  equal  parts.  In  practice  the  fixed  temperatures 
chosen  are  usually  those  of  melting  ice  and  of  boiling 
water  at  a  pressure  of  760  millimeters  of  mercury. 

On  the  Centigrade  scale  the  temperature  of  melting 
ice  is  marked  o°  and  the  temperature  of  boiling  water 
1 00°,  the  length  of  tube  between  these  marks  being 
divided  into  one  hundred  equal  parts.  On  the  absolute 
scale  the  melting  point  of  ice  is  marked  273°,  the 
boiling  point  of  water  373°,  and  the  space  between 
graduated  into  one  hundred  equal  parts.  On  the 
Fahrenheit  scale,  which  is  unfortunately  in  general  use 
in  our  country,  the  melting  point  of  ice  is  32°,  the 
boiling  point  of  water  212°,  and  the  space  between 
divided  into  180  equal  parts.  Nine  degrees  of  the 
Fahrenheit  scale  are  accordingly  equivalent  to  five 
degrees  of  the  Centigrade  scale.  Starting  at  the 
Centigrade  zero,  the  Fahrenheit  reading  is  32°,  then 
at  5°  C  the  reading  will  be  41°  F.,  at  10°  C.  50°  F., 
and  so  following. 


HEAT  181 


Comparison  of  Fahrenheit  and  Centigrade  Scaled 

— To  plot  a  curve  showing  the  comparative  readings 
of  the  Fahrenheit  and  Centigrade  thermometers,  pro- 
ceed as  follows: 

Take  a  piece  of  cross-section  paper,  and  beginning 
at  the  lower  left-hand  corner  number  the  lines  along 
the  vertical  side  of  the  paper  from  o  to  100,  and  along 
the  bottom  edge  from  o  to  212,  or  as  far  as  your 
paper  will  permit. 

Begin  at  32  on  the  bottom  line  (which  is  zero  on 
the  vertical  scale)  and  indicate  by  crosses  on  the  paper 
several  corresponding  points  on  the  two  temperature 
scales.  Thus  15°  on  the  Centigrade  scale  corresponds 
to  59°  on  the  Fahrenheit  scale,  35°  on  the  Centigrade 
to  95°  on  the  Fahrenheit,  and  60°  on  the  Centigrade 
to  140°  on  the  Fahrenheit  scale. 

Draw  a  line  through  these  corresponding  points,  and 
it  will  enable  you  to  transform  a  reading  from  one 
thermometer  scale  to  the  other  at  a  glance. 

Referring  to  your  curve,  what  Fahrenheit  temperature 
corresponds  to  20°  C.  ? 

At  what  temperature  below  zero  are  the  readings  of  the 
two  thermometer  scales  the  same  ? 

To  Test  the  Fixed  Points  of  a  Thermometer. 

LABORATORY  EXERCISE  57. — Support  the  thermometer  in  a 
clamp  with  its  bulb  in  a  large  funnel  or  other  vessel  from 
which  water  will  drain  off.  Pack  the  vessel  around  the 
thermometer  bulb  and  nearly  to  the  zero  point  with  shaved 
or  finely  broken  ice.  Read  the  thermometer,  estimating 
tenths  of  a  degree,  at  intervals  of  about  a  minute.  When 
three  successive  readings  are  the  same,  record  the  tempera- 
ture indicated,  and  the  error  in  the  location  of  the  zero 
point. 

Pour  clean  water  into  the  small  kerosene  can  used  as  a 
boiler  in  Laboratory  Exercise  49.  Pass  the  thermometer 
whose  zero  point  you  have  just  determined  through  a  cork 


i82  PHYSICS 

which  should  be  fitted  into  the  neck  of  the  can.  Push  the 
thermometer  down  into  the  can  until  its  bulb  is  only  one  or 
two  centimeters  above  the  water,  or  until  the  100  mark  is 
just  above  the  cork.  Do  not  let  the  bulb  dip  into  the  water. 
Leave  the  spout  of  the  can  open  for  the  escape  of  the  steam, 
and  boil  the  water  vigorously  over  a  flame.  When  the 
thermometer  reading  has  become  stationary  for  two  minutes, 
read  the  boiling  point  of  the  water  to  one  tenth  of  a  degree. 

Take  the  barometer  reading.  Allowing  a  change  of  tem- 
perature in  the  boiling  point  of  o°.  37  C.  for  a  change  of  one 
centimeter  in  the  barometric  height,  calculate  the  boiling 
point  of  water  at  standard  pressure  as  indicated  by  your 
thermometer.  Calculate  the  error  in  your  thermometer  at 
100°. 

Remove  the  thermometer  from  the  steam,  repack  it  in 
ice,  and  determine  its  zero  point  again. 

Glass  after  being  expanded  contracts  very  slowly,  and  the 
zero  point  of  a  thermometer  is  usually  changed  for  some 
time  after  it  has  been  heated  to  the  boiling  point. 

Calibration  of  Thermometer  Tube. — The  graduation 
of  a  thermometer  tube  is  based  upon  the  assumption 
that  the  tube  is  of  uniform  bore.  In  the  manufacture 
of  thermometers  the  tube  is  calibrated  by  moving  a 
short  mercury  column  along  the  tube  and  measuring 
its  length  in  different  parts  of  the  tube.  This  same 
determination  can  be  made  with  a  finished  thermom- 
eter, but  it  is  attended  with  difficulty  and  is  not  so 
satisfactory  as  the  comparison  of  the  thermometer  with 
a  standard  thermometer  whose  corrections  are  known. 
This  comparison  is  made  by  placing  the  two  thermom- 
eter bulbs  side  by  side  immersed  in  water  which  is  very 
slowly  warmed  and  constantly  stirred  and  reading 
simultaneously  the  temperature  from  the  two  thermom- 
eters. If  a  very  accurate  comparison  is  required,  the 
readings  must  be  made  while  the  water  is  falling  in 
temperature  as  well  as  rising. 


HEAT  183 


CALORIMETRY 

Definition. — The  measurement  of  heat  quantities  is 
known  as  Calorimetry. 

The  Heat  Unit. — For  the  measurement  of  heat 
quantities  a  thermal  unit  is  necessary,  just  as  a  unit  of 
length  is  necessary  for  measuring  distances.  In  labora- 
tory practice  the  thermal  unit  generally  used  is  called 
the  Gram-calorie.  It  is  the  quantity  of  heat  necessary 
to  raise  the  temperature  of  one  gram  of  water  one 
degree  Centigrade.  Within  the  limits  of  accuracy  of 
our  experiments  this  quantity  is  the  same  whether  we 
raise  the  temperature  of  the  water  from  o°  to  i°,  or 
from  90°  to  91°,  though  by  careful  measurements  a 
difference  may  be  shown. 

Heat  Capacity. — By  the  heat  capacity  of  a  body  we 
mean  the  number  of  heat  calories  required  to  change 
its  temperature  one  degree  Centigrade. 

Heat  Capacity  of  a  Calorimeter. 

LABORATORY  EXERCISE  58. — A  tin  can  holding  about  a 
pint  and  set  in  a  wooden  or  pasteboard  box  and  loosely 
packed  round  with  wool  or  hair  may  be  used  as  a  Calorim- 
eter, or  a  glass  beaker  holding  about  400  cubic  centimeters 
may  be  set  inside  a  beaker  of  the  next  larger  size  and  a  little 
wool  or  cotton  distributed  in  the  space  between  to  prevent 
convection  currents  in  the  air  and  be  used  for  the  same  pur- 
pose. If  very  hot  water  is  never  used  in  the  calorimeter,  a 
cover  is  unnecessary. 

Pour  about  200  cubic  centimeters  of  weighed  or  measured 
water  in  the  beaker  at  a  temperature  about  ten  degrees 
below  the  room  temperature.  Stir  the  water  with  a  ther- 
mometer, and  take  its  temperature  when  the  mercury  col- 
umn has  become  stationary,  estimating  tenths  of  a  degree. 
From  another  vessel  containing  water  about  ten  degrees 
warmer  than  the  air,  and  whose  temperature  is  known  to  a 


i84  PHYSICS 

tenth  of  a  degree,  pour  in  about  200  cubic  centimeters  of 
water.  Stir  rapidly  and  take  the  temperature  to  tenths  of 
a  degree  as  soon  as  the  thermometer  comes  to  rest. 

Weigh  or  measure  the  water  again  to  find  how  much  you 
have  poured  in. 

Assuming  that  water  gains  or  loses  one  gram-calorie  of 
heat  per  gram  for  each  degree  of  temperature  change,  what 
should  have  been  the  temperature  of  the  resulting  water  ? 

How  much  heat  was  lost  to  the  air  and  the  calorimeter  ? 
How  much  heat  was  required  to  change  the  temperature  of 
the  calorimeter  one  degree  ?  Call  this  the  heat  capacity  of 
the  calorimeter. 

(Thus  195  grams  of  water  are  warmed  10°,  requiring  1950 
calories;  200  grams  of  water  are  cooled  10°,  losing  2000 
calories.  Heat  lost  to  calorimeter  and  to  air  50  calories. 
Calorimeter  warmed  10°,  capacity  of  calorimeter  5  calories.) 

Make  three  determinations,  and  compare  results.  What 
is  the  mean  of  the  three  ?  What  the  greatest  variation  from 
this  mean  ?  What  the  extreme  variation  between  any  two 
determinations  ?  How  great  an  error  in  the  final  tempera- 
ture reading  of  your  thermometer  would  account  for  this 
error  ?  If  you  make  a  mistake  of  one  tenth  of  a  degree  in 
the  final  reading  of  your  thermometer,  how  great  an  error  in 
calories  will  it  produce  ? 

Determination  of  Latent  Heat  of  Fusion  of  Ice. 

LABORATORY  EXERCISE  59. — We  have  seen  that  a  consider- 
able quantity  of  heat  is  required  to  change  ice  into  water 
without  raising  its  temperature.  This  heat  is  required  to 
give  to  the  molecules  the  additional  potential  energy  of  the 
liquid  state,  and  is  called  the  Latent  Heat  of  Fusion.  We 
wish  to  find  how  many  calories  of  heat  become  latent  in 
melting  one  gram  of  ice. 

Counterpoise  your  calorimeter  on  the  platform  balance, 
and  pour  in  300  or  400  grams  of  water  warmed  to  about 
60°  C. 

Have  ready  about  100  or  150  grams  of  finely  broken  ice 
drying  on  a  cloth.  Take  the  temperature  of  the  water 
accurately,  put  in  the  dry  ice  and  stir  until  it  melts.  Take 
the  temperature  again.  Weigh  to  see  Jiow  many  grams  of 
ice  you  have  addecl. 


HEAT 


185 


Calculate : 

(a)  How  many  calories  of  heat  were  given  up  by  the 
cooling  water. 

(3)  How  many  calories  were  given  up  by  cooling  calorim- 
eter. 

(c)  How  many  calories  were  used  up  in   warming  the 
melted  ice  from  zero  to  the  final  temperature. 

(d)  How  many  calories  were  required  to  melt  the  ice. 

(*)  How  many  calories  were  required  to  melt  one  gram 
of  the  ice. 

Make  three  determinations  and  take  the  mean.  The 
latent  heat  of  fusion  of  ice  is  taken  as  80  calories.  What  is 
the  error  of  your  result  ?  By  what  per  cent  of  the  true  value 
is  it  wrong  ? 

How  many  grams  of  ice  could  be  melted  by  cooling  500 
grams  of  water  from  70°  C.  to  o°  C.  ? 

Determination  of  Latent  Heat  of  Vaporization  of 
Water. 

LABORATORY  EXERCISE  60. — The  number  of  calories  of 
heat  required  to  change  one  gram  of  water  into  steam  with- 
out increasing  its  temperature  is  called 
the  Latent  Heat  of  Vaporization  of  Water. 

To  provide  steam  free  from  water,  pass 
the  steam  from  the  boiler  through  a  trap 
made  of  a  side-neck  test  tube  or  a  piece 
of  large  glass  tubing  fitted  with  corks  as 
shown  in  Fig.  52.  If  the  latter  device 
is  used,  the  end  of  the  delivery  tube 
should  be  pushed  past  the  end  of  the 
tube  which  brings  the  wet  steam  from  the 
boiler,  so  that  all  the  water  may  be  left 
in  the  trap.  The  boiler  may  be  the  one 
used  in  Laboratory  Exercises  49  and  57. 

Counterpoise  the  calorimeter  as  before, 
pour  in  about  300  grams  of  water,  if  FlG>  52- 

possible,  cooled  with  ice  to  about  5°  C.  When  dry  steam 
is  escaping  rapidly  from  the  delivery  tube  of  your  boiler, 
take  the  temperature  of  the  cold  water,  and  then  suddenly 
insert  the  delivery  tube  into  the  cold  water  and  allow  the 
steam  to  condense  until  the  water  ha§  been  heated  up  to  50° 


1 86  PHYSICS 

or  60°.  Withdraw  the  delivery  tube,  weigh  the  water  to 
find  out  how  many  grams  of  steam  have  been  condensed, 
and  calculate  the  latent  heat  of  vaporization  of  water. 

The  latent  heat  of  steam  is  given  in  the  tables  as  536 
calories.  What  is  the  error  of  your  determination  ? 

How  much  ice  could  be  melted  by  condensing  100  grams 
of  steam  and  cooling  it  to  o°  C.  ? 

Fifty  grams  of  wet  snow  was  melted  and  warmed  to  10°  C. 
by  5  grams  of  steam.  What  part  of  the  wet  snow  was  ice 
and  what  part  was  water  ? 

Specific  Heat. — The  number  of  calories  required  to 
change  the  temperature  of  one  gram  of  a  substance 
through  one  degree  Centigrade  is  called  Specific  Heat 
of  the  Substance. 

Determination  of  Specific  Heat  of  Lead  Shot. 

LABORATORY  EXERCISE  61. — Put  500  grams  of  fine  shot  in 
a  small  flask,  and  place  the  flask  in  boiling  water.  Insert  a 
thermometer  bulb  in  the  interior  of  the  mass  of  shot,  and 
note  its  temperature  when  it  becomes  stationary.  Put  about 
200  grams  of  weighed  water  in  the  calorimeter  (preferably  a 
few  degrees  below  the  room  temperature),  and  take  its  tem- 
perature. Pour  the  shot  quickly  into  the  water,  stir,  and 
take  the  temperature  as  soon  as  it  becomes  constant. 

Calculate  the  heat  capacity  of  500  grams  of  shot. 

Calculate  the  specific  heat  of  shot. 

Determination  of  Specific  Heat  of  a  Liquid. 

LABORATORY  EXERCISE  62. — A  "  Calorifer  "  is  prepared  as 
follows:  A  glass  bulb  about  one  inch  in  diameter  has 
attached  a  glass  tube  of  about  one  millimeter  bore.  (Such 
bulbs  and  tubes  are  bought  as  air  thermometers.)  The 
bulb  is  carefully  filled  with  clean  mercury  by  successive 
heatings  to  drive  out  the  air  and  allowing  mercury  to  be 
drawn  in  as  the  contained  air  cools  and  contracts.  The 
mercury  column  can  always  be  let  down  into  the  bulb  by 
using  a  fine  wire.  Make  a  mark  on  the  stem  at  about  the 
point  to  which  the  mercury  column  will  rise  at  30°  C. , 
and  another  mark  just  below  the  place  to  which  the  mercury 
column  will  rise  at  100°  C. 

A  calorifer  in  which  the  tube  has  been  exhausted  and 
sealed  off  is  shown  in  Fig.  53. 


HEAT 


187 


Place  the  mercury  bulb  in  boiling  water  and  let  the 
mercury  expand  and  rise  above  the  upper 
mark.  Put  200  grams  of  cold  water  in  the 
calorimeter,  take  its  temperature,  raise  the 
mercury  bulb  by  its  stem  out  of  the  boiling 
water,  dry  it  quickly,  and  at  the  instant  when 
the  mercury  column  has  fallen  to  the  upper 
mark  immerse  it  in  the  cold  water  in  the 
calorimeter.  Hold  it  by  the  stem,  and  lift 
it  out  of  the  water  at  the  instant  when 
the  top  of  the  mercury  column  reaches  the 
lower  mark.  Take  the  temperature  of  the 
water  and  determine  how  many  heat  calories 
the  mercury  has  given  off  while  its  column 
was  falling  the  distance  between  the  two 
marks.  This  is  the  heat  value  of  your 
calorifer. 

Put  100  grams  of  gasoline  in  your  cal- 
orimeter and  by  means  of  your  calorifer 
determine  its  specific  heat;  Do  not  allow 
the  flame  to  come  near  your  gasoline. 

Specific  Heats  of  Gases. — In  our  dis- 
cussion of  the  kinetic  gas  theory  (page 
85)  we  saw  that  a  gas  heated  under  constant  pressure 
will  expand  and  do  work,  and  that  the  work  in  ergs 
done  by  the  expanding  gas  may  be  calculated  by 
multiplying  its  increase  of  volume  in  cubic  centimeters 
by  the  pressure  in  dynes  under  which  it  expands ;  that 

1S,     W  =    (V2  -   Vjp. 

It  follows  from  what  we  have  learned  of  the  relation 
between  heat  and  work  that  the  work  done  by  the 
^expanding  gas  must  require  the  expenditure  of  heat 
and  that  the  gas  will  require  more  heat  to  raise  its 
temperature  by  a  given  amount  when  it  is  allowed  to 
expand  under  pressure  than  it  will  when  it  is  confined 
to  a  constant  volume.  Gases  accordingly  have  two 
specific  heats,  a  specific  heat  at  constant  volume,  and 


FIG.  53. 


1 88  PHYSICS 

a    specific    heat    at  constant  pressure.      The  latter  is 
greater  than  the  former. 

Relation  between  the  Two  Specific  Heats  of  Air. 

LABORATORY  EXERCISE  63. — Fit  a  flask  of  about  one-half 
liter  capacity  with  an  air-tight  stopper  through  which  a 
thermometer  is  passed.  The  flask  should  contain  only 
thoroughly  dry  air,  and  the  stopper  should  be  air-tight. 

Boil  a  sufficient  quantity  of  water  in  a  convenient  vessel, 
and  while  the  water  is  boiling  rapidly  read  the  thermometer 
and  then  lower  the  flask  suddenly  into  the  water  to  a  mark 
made  by  fastening  a  wire  or  string  around  the  neck  of  the 
flask.  Note  by  the  second-hand  of  a  watch  the  instant  when 
the  flask  is  plunged  into  the  water.  Hold  the  flask  in  the 
water  until  the  temperature  of  the  enclosed  air  has  risen 
forty  or  fifty  degrees.  It  will  probably  be  necessary  to  hold 
the  cork  tightly  in  place,  as  the  increased  pressure  of  the 
contained  air  may  loosen  it.  Note  the  instant  at  which  the 
flask  is  withdrawn  from  the  water.  Hold  it  until  the  mer- 
cury ceases  to  rise  in  the  thermometer,  which  will  be  a  few 
seconds  after  the  flask  is  withdrawn  from  the  water. 

Record  the  time  during  which  the  flask  was  receiving  heat 
from  the  water  and  the  rise  of  the  thermometer. 

Loosen  the  stopper  so  that  as  the  air  in  the  flask  expands  it 
may  escape  into  the  outside  air,  and  after  its  temperature  has 
fallen  to  that  of  the  first  experiment  repeat  the  experiment, 
holding  the  flask  in  the  water  for  exactly  the  same  length  of 
time  as  before  and  noting  the  rise  of  temperature  of  the 
enclosed  air. 

In  which  case  was  the  greater  quantity  of  air  heated  in  the 
flask  ?  In  which  case  was  its  temperature  raised  the  more  ? 
Assuming  that  the  flask  received  the  same  amount  of  heat 
from  the  water  in  both  cases,  in  which  experiment  was  the 
specific  heat  of  air  greater  ? 

By  how  many  cubic  centimeters  would  a  half  liter  of  air 
under  standard  pressure  expand  in  being  heated  from  20°  C. 
to  60°  C.  ?  How  many  ergs  of  work  would  it  do  in 
expanding  ? 

Energy  Value  of  the  Calorie. — In  referring  to  Dr. 
Joule's  experiments  on  the  relation  of  heat  to  work 
(page  142),  it  was  stated  that  he  found  that  773.64  foot- 


HEAT  189 

pounds  of  work  when  changed  into  heat  would  raise 
the  temperature  of  one  pound  of  water  by  one  degree 
Fahrenheit. 

A  Fahrenheit  degree  is  five  ninths  of  a  Centigrade  degree; 
how  many  foot-pounds  of  energy  would  be  required  to  raise 
the  temperature  of  a  pound  of  water  one  degree  Centigrade  ? 

To  what  height  can  a  mass  of  water  be  raised  by  the 
energy  required  to  warm  it  one  degree  Centigrade  ? 

The  Yosemite  Fall  is  2548  feet  high.  How  much  warmer 
should  the  water  be  in  the  stream  below  the  fall  than  in  the 
stream  above  ? 

The  mean  value  of  the  best  determinations  of  Joule's 
equivalent  shows  that  the  energy  required  to  warm  a 
gram  of  water  by  one  degree  Centigrade  is  sufficient 
to  raise  a  gram  weight  427  meters  in  the  mean  latitude 
of  the  United  States.  Since  the  weight  of  a  gram 
varies  with  variations  in  gravitation  upon  different  parts 
of  the  earth,  while  the  heat  energy  of  a  gram  calorie  is 
not  variable,  it  is  desirable  to  be  able  to  state  the 
energy  equivalent  of  the  gram  calorie  in  invariable 
energy  units.  Expressed  in  the  C.G.S.  system,  this 
value  is  taken  as  forty-two  million  ergs.  This  quan- 
tity is  accordingly  known  as  the  dynamical,  or  the 
mechanical,  equivalent  of  the  heat  unit,  and  is  Joule's 
Equivalent  expressed  in  ergs. 

What  part  of  a  gram  calorie  is  used  to  do  the  work  of 
expansion  of  a  liter  of  air  under  standard  pressure  when 
warmed  from  20°  C.  to  70°  C.? 

Explain  the  apparent  loss  of  kinetic  energy  of  the  two 
putty  balls  referred  to  on  page  136. 

HEAT   ENGINES 

Definition. — Machines  in  which  heat  is  transformed 
into  mechanical  energy  and  applied  to  the  performance 
of  work  are  known  as  Rent  Engines.  The  steam 


190 


PHYSICS 


engine  is  the  best  known  and  most  important  type  of 
heat  engines. 

The  Steam  Engine. — The  steam  engine  is  a  machine 
in  which  the  expansive  force  of  steam  is  used  to  drive 
a  piston  forward  and  back  in  a  cylinder,  while  the 
motion  of  the  piston  is  utilized  to  drive  other  machines 
or  to  propel  the  engine. 


FIG.  54- 

The  principal  working  parts  of  the  modern  steam 
engine  are  shown  in  Figs.  54  and  55.  In  Fig.  54  the 
cylinder  and  connected  parts  are  shown  in  plan  (that 
is,  you  are  supposed  to  be  looking  down  upon  them), 
and  in  Fig.  5  5  the  engine  is  shown  in  elevation.  The 
lettering  of  parts  is  the  same  in  both  figures. 


HEAT  IQI 

Thus  Ay  Fig.  54,  represents  the  cylinder  in  which  the 
tight-fitting  piston  B  is  driven  back  and  forth  as  the 
steam  enters  the  cylinder  alternately  on  one  side  of  it  or 
on  the  other.  Attached  to  one  side  of  the  cylinder  is  the 
steam  chest,  or  valve  chest,  c,  from  which  the  steam  is 
admitted  to  the  cylinder  through  openings  at  its  ends 
called  steam  ports.  These  ports  are  alternately  con- 
nected with  the  steam  chest  and  with  the  exhaust  pipe 
e  by  means  of  the  slide  valve  d. 

In  Fig.  54  the  piston  is  represented  as  moving 
toward  the  left,  as  shown  by  the  arrow  near  the  piston 
rod  C.  The  slide  valve  is  also  moving  in  the  same 
direction,  but  is  nearly  at  the  end  of  its  stroke.  The 
steam  port  back  of  the  piston  is  in  communication  with 
the  steam  chest,  while  the  steam  port  in  front  of  the 
piston  is  in  communication  with  the  outside  air  or  the 
condensing  chamber  through  the  exhaust  pipe.  The 
piston  is  accordingly  receiving  the  full  pressure  of  the 
steam  from  the  boiler  on  one  side,  and  a  pressure  of 
an  atmosphere  or  less  on  the  other  side. 

Before  the  piston  reaches  the  end  of  its  stroke,  the 
slide  valve  will  be  drawn  back,  closing  the  port  through 
which  the  steam  now  enters,  and  an  instant  later  the 
other  port  will  be  opened  into  the  steam  chest  and  the 
motion  of  the  piston  will  be  reversed. 

In  Fig.  55  a  side  view  of  the  engine  is  shown. 
The  valve  chest  with  its  slide  valve,  its  eccentric  red P 
and  the  eccentric  wheel  E  as  it  is  mounted  on  the  main 
shaft  L  are  shown  below.  Their  position  in  the  engine 
is  on  the  side  opposite  the  observer.  The  steam  pipe 
a  is  represented  as  turned  upward  after  leaving  the 
valve  chest,  and  at  b  is  shown  the  position  of  the 
throttle  valve  by  which  the  supply  of  steam  from  the 


PHYSICS 


HEAT  193 

boiler  may  be  regulated  or  cut  off.  The  exliaust  pipe 
e  is  represented  as  turned  downward  below  the 
cylinder. 

The  piston  rod  C  is  shown  with  its  parallel-motion 
guides  W  at  its  junction  with  the  connecting  rod  G. 
The  connecting  rod  is  attached  by  means  of  a  boxing 
to  the  crank  pin  M,  thus  enabling  it  to  turn  the  crank, 
which  is  keyed  to  the  main  shaft  L. 

The  heavy  fly-ivheel  mounted  on  the  main  shaft  is  to 
steady  the  motion  of  the  shaft.  During  a  part  of  its 
revolution  it  is  being  accelerated  by  the  energy  derived 
from  the  piston,  and  during  another  part  it  is  giving 
off  its  energy  to  accelerate  the  motion  of  the  piston. 
In  this  way  the  jerky  motion  of  the  piston  is  trans- 
formed into  the  steady  motion  of  the  main  shaft. 

The  fly-wheel  may  also  be  used  as  a  driving-wheel, 
in  which  case  it  carries  the  belt  by  which  the  energy 
of  the  engine  is  transferred  to  another  machine. 

High-pressure  and  Low-pressure  Engines.  —  En- 
gines in  which  the  exhaust  pipe  opens  into  the  external 
air  (or,  as  in  the  railroad  locomotive,  into  the  chimney 
of  the  furnace)  are  known  as  high-pressure  engines. 
In  such  engines  the  piston  must  always  be  forced 
against  the  pressure  of  the  atmosphere  in  addition  to 
the  other  load  it  must  move.  In  low-pressure,  or  con- 
densing, engines  the  exhaust  pipe  opens  into  an 
exhausted  air-tight  vessel  called  the  condenser,  where 
the  steam  is  condensed  by  a  spray  of  cold  water.  The 
heated  water  from  the  condenser  is  then  pumped  into 
the  boiler  and  used  again  in  the  production  of  steam. 

The  Gas  Engine. — Another  form  of  heat  engine 
which  is  very  extensively  used  is  the  gas  engine.  In 
this  engine  a  mixture  of  air  and  coal  gas  or  gasoline 


i94  PHYSICS 

vapor  in  proper  proportions  is  introduced  into  the 
cylinder,  the  admission  is  cut  off,  and  the  mixture 
exploded  by  an  electric  spark.  The  explosion  develops 
a  sufficient  quantity  of  heat  to  raise  the  enclosed  gas  to 
a  high  temperature,  and  the  expansion  of  the  heated 
gases  drives  the  piston  before  them  until  the  stroke  is 
completed.  The  gaseous  products  of  the  combustion 
are  then  expelled  by  the  return  stroke  of  the  piston. 
The  second  stroke  of  the  piston  allows  a  new  charge 
of  mixed  gases  to  enter  the  cylinder,  the  return  stroke 
compresses  them  and  they  are  then  exploded  by 
another  spark.  Thus  the  piston  makes  two  strokes 
and  returns,  giving  two  complete  revolutions  of  the 
main  shaft,  for  each  explosion.  The  piston  in  the  gas 
engine  accordingly  receives  one  impulse  while  that  of 
the  steam  engine  receives  four. 

Fig.  56  shows  a  plan  of  a  gas  engine  in  which  the 
parts  are  lettered  like  the  corresponding  parts  of  the 
steam  engine  in  Figs.  54  and  55.  A  represents  the 
cylinder  with  only  one  cylinder  head,  instead  of  two 
as  in  the  steam  engine.  B  represents  the  bucket- 
shaped  piston,  which,  on  account  of  its  long  bearing 
on  the  cylinder  wall,  does  not  need  a  piston  rod  and 
parallel-motion  guides.  The  connecting  rod  G  is 
hinged  to  the  piston  by  the  steel  bolt  D,  known  as  the 
cross-head  gudgeon,  which  passes  through  the  head  of 
the  connecting  rod,  and  upon  which  the  head  of  the 
connecting  rod  turns  as  the  other  end  turns  upon  the 
crank  pin. 

The  mixed  gases  enter  the  chamber  c,  from  which, 
by  the  opening  of  the  valve  d,  they  enter  the  explosion 
chamber  E,  where  they  are  ignited  by  the  sparking 
apparatus  F,  which  is  joined  to  an  induction  coil  and 


HEAT 


'95 


196  PHYSICS 

a  voltaic  battery.  The  admission  valve  d  is  opened  by 
the  cam  J  which  is  mounted  on  the  governor  shaft  TV, 
and  which  is  controlled  by  the  governor  S  so  as  to  vary 
the  amount  of  the  entering  gas.  The  products  of  com- 
bustion are  removed  through  the  valve  P  which  is 
opened  at  each  revolution  of  the  governor  shaft  by 
means  of  the  crank  Q  and  the  cam  R. 

On  account  of  the  great  amount  of  heat  generated 
by  the  explosion  of  the  gases,  it  is  necessary  to  provide 
the  cylinder  with  a  cooling  apparatus.  In  the  figure 
the  spaces  marked  H  are  cavities  for  the  circulation  of 
cold  water  about  the  cylinder. 

In  Fig.  57  the  parts  are  lettered  as  in  Fig.  56.  The 
pipe  a  is  for  the  entering  gas.  At  b  is  shown  the  posi- 
tion of  the  throttle  valve,  and  the  exhaust  pipe  is  shown 
at  e.  The  pipes  //"and  H'  are  for  the  water  circulation 
which  cools  the  cylinder. 

Efficiencies  of  Engines. — The  efficiency  of  the  best 
gas  engines  is  nearly  twice  as  great  as  that  of  the  best 
steam  engines;  that  is,  nearly  twice  as  large  a  per- 
centage of  the  total  energy  of  combustion  of  the  fuel 
used  is  utilized  in  the  gas  engine  as  in  the  steam 
engine.  In  the  latter  a  large  part  of  the  heat  is  neces- 
sarily lost  in  the  furnace  and  boiler  before  it  reaches 
the  cylinder,  while  in  the  former  the  combustion  takes 
place  and  the  heat  is  generated  in  the  cylinder  itself. 
Still  the  loss  of  energy  is  very  great  in  the  gas  engine. 
A  very  high  temperature  is  developed  by  the  explosion, 
the  cylinder  walls  are  heated,  and  the  water  which 
circulates  through  the  cylinder  jackets  carries  away  a 
great  deal  of  heat.  The  gases  which  escape  through 
the  exhaust  pipe  have  not  transformed  all  their  molec- 
ular energy  into  mechanical  energy,  and  they  are 


HEAT 


197 


198  PHYSICS 

accordingly  still  hot.  Fully  three  fourths  of  the  energy 
liberated  by  the  explosion  is  used  up  in  these  different 
ways,  so  that  a  very  good  gas  engine  does  not  trans- 
form more  than  25  per  cent  of  the  total  energy  of  the 
combustion  into  mechanical  work. 

The  efficiency  of  a  steam  engine  rarely  reaches  1 5 
per  cent. 

PROBLEMS. — A  steam  engine  of  10  horse-power  is  used  to 
raise  water  from  a  well  50  feet  deep.  If  a  gallon  of  water 
weighs  8.3  pounds,  how  many  gallons  per  minute  can  be 
raised  by  the  engine  ? 

A  5 -horse-power  engine  works  a  paddle  wheel  in  a  vessel 
of  water  containing  10  kilograms.  Neglecting  the  heat  given 
off  to  the  containing  vessel,  how  long  will  it  take  to  raise 
the  temperature  of  the  water  50°  Centigrade  ? 

If  the  efficiency  of  the  above  engine  is  10  per  cent,  how 
many  calories  of  heat  are  given  off  by  the  coal  during  the 
experiment  ? 


PART  IV 

WAVE-MOTION   AND   SOUND 
SOUND 

Scope  of  the  Subject. — The  form  of  energy  trans- 
ference known  as  Wave-motion  is  best  studied  in  its 
relation  to  the  phenomena  of  Sound  and  Light.  Sound 
and  Light  differ  from  other  branches  of  Physics  in  that 
they  involve  both  a  physical  and  a  physiological  side. 
The  physical  side  of  the  subject  of  Sound  is  principally 
concerned  with  wave-motions  in  elastic  bodies.  The 
physiological  side  is  concerned  with  the  sensations  pro- 
duced in  the  hearing  organ  by  means  of  these  wave- 
motions. 

VIBRATION   OF   SOUNDING   BODIES 

First  Law  of  Sound. — The  fundamental  proposition 
in  the  study  of  Sound  is  that  All  sounding  bodies  are  in 
a  state  of  vibration.  These  vibrations  may  be  observed 
in  a  number  of  characteristic  sounding  bodies  by  means 
of  the  following  experiments. 

Experiments  on  Sound  Vibration. 

LABORATORY  EXERCISE  64.  —  a.  Sound  a  tuning  fork  by 
striking  it  against  a  cork  or  against  the  knee,  and  feel  the 
vibrations  of  the  prongs.  Of  the  stem.  Touch  the  prongs 

199 


200  PHYSICS 

and  the  stem  to  water.  What  proofs  of  vibration  do  you 
observe  ?  Stop  the  vibrations  with  the  fingers.  Can  you 
make  the  fork  sound  when  it  is  not  in  vibration  ? 

b.  Stretch  a  fine  wire  by  means  of  piano  pegs  on  a  board 
or  a  sounding  box,  and  cause  the  wire  to  sound  by  bowing 
it  with  a  violin  bow.      Prove  that  the  wire  is  in  vibration 
while  it  is  sounding.      Explain  your  method  of  proof. 

c.  Fill  a  round  glass  vessel,  as  a  finger  bowl,  or  a  wide 
sugar  bowl  with  a  smooth  rim,  half  full  of  water  and  make 
it  sound  by  bowing  across  its  rim.     Use  plenty  of  rosin  on 
the  bow.      Does  the  glass  vibrate  ?     How  do  you  know  ? 

d.  A    round    or    square   brass    plate  with  smooth    edges 
fastened  rigidly  in  a  horizontal   position  by  a  screw  or  a 
clamp  at  its  center  is  called  a  Chladni's   Plate.      Sound  the 
plate  by  bowing  across  its  edge  with  a  well-rosined  bow. 
While  it  is  sounding;  sprinkle  sand  upon  the  plate.      Is  it  in 
vibration  ?     Does  it  vibrate  as  a  whole,  or  are  there  places 
of  rest  ?     Must  the  vibrations  on  opposite  sides  of  the  places 
of  rest  be  in  the  same,  or  in  opposite  directions  ? 

e.  A  wooden  organ  pipe  with  one  thin  side  may  be  laid 
upon  the  table  with  the  thin  side  uppermost.     Sound  the 
pipe  by  blowing,   and   sprinkle  sand    upon  the   thin   side. 
.What  evidences  of  vibration  in  the  pipe  do  you  detect  ? 

f.  A  glass  tube  three  or  four  feet  long  and  from  a  half  inch 
to  an  inch  in  internal  diameter  is  held  in  a  horizontal  posi- 
tion by  a  clamp  *  at  the  middle  of  the  tube.     Cork  one  end 
of  the  tube  and  scatter  along  the  inside  of  the  tube  dry  cork 
dust,  made  by  filing  a  cork  which  has  been  thoroughly  baked 
in   an  oven.      Dampen  a  piece  of  flannel   with  water,    and 
holding  it  in  the  hand  grasp  the  tube  with  it  and  stroke  it 
lengthwise  until  it  gives  off  a  clear  sound.     What  evidences 
of  vibration  do  you  see  in  the  cork  dust  ? 

Remove  the  cork  from  the  end  of  the  tube  and  cause  it  to 
sound  as  before.  Does  the  cork  have  anything  to  do.  with 
the  vibrations  of  the  cork  dust  in  the  tube  ?  If  the  tube 
vibrates  lengthwise,  what  effect  will  the  cork  in  its  end  have 
upon  the  air  inside  ?  If  the  ends  of  the  tube  vibrate  side- 
wise,  will  the  cork  set  the  inside  air  in  vibration  ?  -What  do 
you  conclude  about  the  nature  of  the  vibrations  of  the  tube  ? 

*  For  clamping  the  tube,  bore  a  hole  slightly  smaller  than  the  tube  in 
a  piece  of  board  about  an  inch  thick  and  two  or  three  inches  wide,  and 


WAVE-MOTION  AND  SOUND 


201 


Observe  carefully  the  peculiar  figures  formed  by  the  dust 
particles  in  the  tube.  These  will  be  considered  later. 

g.  A  metal  or  cardboard  disc  with  a  row  of  round  holes 
spaced  at  equal  distances  near  its  edge  and  mounted  so  that 
it  can  be  set  in  rapid  rotation  is  called  a  Disc  Siren.  Set 
the  disc  in  rapid  rotation  and  blow  through  the  holes  by 
means  of  a  piece  of  rubber  tubing.  Can  you  produce  a  con- 
tinuous sound  in  this  way  ?  What  vibrations  may  be 
regarded  as  the  cause  of  the  sound  ?  Can  sound  be  caused 
by  the  vibrations  of  a  gaseous  body  ? 

All  of  the  above  experiments  show  that  sound  is 
associated  with  the  vibrations  of  material  bodies.  In 
the  following  experiments  we  wish  to  find  what  kinds 
of  bodies  may  transmit  these  vibrations.  "x^y 

Transmission  of  Vibrations  by  Solids,  Liquids,  an<J 

Gases. 

LABORATORY  EXERCISE  65. — Sound  a  tuning  fork  and  hold 

with  a  saw  cut  a  slit  from  the  end  of  the  board  into  the  hole.     This  will 
allow  the  hole  to  spread  so  that  the  tube  can  be  pushed  through  it.     Push 


FIG.  58. 

the  tube  through  to  its  middle,  and  fasten  it  in  position  by  drawing  the 
two  sides  of  the  slit  together  by  means  of  a  screw,  us  shown  in  Fig.  58. 
Then  screw  or  clamp  the  board  to  the  table  so  that  the  tube  is  horizontal. 


202  PHYSICS 

the  end  of  its  stem  tightly  against  the  table.  Does  the  fork 
continue  to  vibrate  as  long  as  when  held  loosely  in  the 
fingers  ?  Why  ?  Note  the  increase  in  the  loudness  of  the 
sound. 

Since  the  vibrating  prongs  set  but  little  air  in  motion,  they 
give  off  their  energy  very  slowly.  When  the  end  of  the  stem 
is  held  against  the  table  the  energy  is  given  off  rapidly  to  the 
table  and  by  it  to  the  air,  and  consequently  more  of  it  enters 
our  ears  in  a  given  time.  We  accordingly  recognize  the 
sound  as  louder. 

Find  a  box,  as  a  cigar  box,  which  sounds  loudly  when 
touched  by  the  stem  of  the  fork.  Hold  the  stem  of  the 
sounding  fork  against  the  end  of  a  short  rod  of  wood,  and 
press  the  other  end  of  the  rod  upon  the  box.  Does  the  rod 
transmit  the  vibrations  of  the  fork  to  the  box  ? 

Try  in  the  same  way  to  pass  the  vibrations  of  the  fork 
through  iron,  glass,  India  rubber,  and  other  substances,  and 
note  which  ones  are  good  transmitters  of  vibrations. 

Place  a  glass  of  water  upon  the  box,  and  holding  the  stem 
of  the  sounding  fork  against  a  small  block  of  wood,  place 
the  block  in  the  water,  taking  care  that  it  does  not  touch 
the  glass.  Are  the  vibrations  of  the  fork  transmitted  by  the 
water  ? 

Two  large  tuning  forks  are  mounted  upon  sounding  boxes 
and  so  adjusted  that  when  one  is  sounded  near  the  other, 
the  other  takes  up  the  sound.  Since  the  second  fork  is  set 
in  vibration  when  it  sounds,  the  vibrations  of  the  first  fork 
must  have  been  transmitted  to  it  by  some  medium. 

Let  another  person  hold  one  of  the  forks  by  its  box  while 
you  stand  near  and  cause  the  other  one  to  sound  loudly  by 
bowing  it  across  one  of  the  prongs.  Are  the  vibrations  of 
the  sounding  fork  transmitted  to  the  other  by  the  intervening 
air  ?  Take  as  many  precautions  as  you  can  to  prevent  the 
transmission  of  the  vibrations  by  solids  or  liquids  and  satisfy 
yourself  whether  sound  vibrations  may  be  transmitted  by  air. 

A  string  telephone  is  constructed  by  stretching  a  piece  of 
animal  membrane,  thin  rubber,  or  parchment  paper  over  the 
end  of  a  small  box  from  which  the  bottom  has  been  removed 
and  connecting  the  center  of  this  membrane  to  a  string  or 
thread.  When  the  string  is  tightly  stretched  between  two 
such  telephones,  a  conversation  can  be  carried  on  over  the 


W AYE-MOTION  AND  SOUND  203 

line.     Explain  the  sound  vibrations  in  the  box  which  is  held 
to  the  ear. 

Vibrations  not  Transmitted  by  a  Vacuum.— The 
above  experiments  show  that  sound  vibrations  may  be 
transmitted  by  solids,  liquids,  or  gases.  That  they 
may  not  be  transmitted  by  a  vacuum  is  shown  as  fol- 
lows: 

A  loud-ticking  watch  or  other  sounding  body  may 
be  placed  upon  a  loose  pad  of  cotton  or  wool  under  the 
receiver  of  an  air-pump  and  the  air  may  be  exhausted 
by  means  of  the  air-pump.  A  noticeable  decrease  of 
the  sound  will  be  observed  as  the  air  in  the  receiver 
becomes  rarefied.  It  is  impossible  with  an  ordinary 
air-pump  to  exhaust  all  the  air  from  the  receiver,  and 
the  sounding  body  cannot  be  supported  so  that  it  will 
not  be  in  contact  with  other  bodies  which  may  carry 
the  vibrations  to  the  outer  air.  Experiments  have  been 
made  in  this  way,  however,  which  show  conclusively 
that  sound  vibrations  are  not  transmitted  by  a  vacuum. 
It  follows  that  sound  vibrations  are  not  transmitted  by 
the  Luminiferous  Ether. 

WAVE-MOTION 

How  Vibrations  are  Transmitted. — We  have  seen 
that  the  energy  of  sound  vibrations  may  be  transmitted 
by  solids,  liquids,  and  gases.  We  now  wish  to  study 
the  manner  in  which  this  energy  is  transmitted  by  the 
bodies  which  serve  as  its  carriers. 

Wave-motion  in  Spring  Cord. 

LABORATORY  EXERCISE  66. — A  long  cord  of  wire  wound  in 
the  form  of  a  spiral  spring  should  have  one  end  attached  to 
a  rigid  support,  preferably  to  a  high  ceiling.  Taking  the 
free  end  of  the  cord  in  the  hand  and  giving  a  quick  jerk  to 
one  side  and  back,  throw  a  short  portion  of  the  cord  into  a 


204  PHYSICS 

loop  .or  kink,  and  notice  that  this  loop  travels  along  the  cord 
from  your  hand  to  the  fixed  end  of  the  cord.  If  both  ends 
of  the  cord  be  held  rigidly  fixed  after  the  loop  is  formed,  it 
may  travel  forward  and  back  several  times  the  length  of  the 
cord  before  its  energy  is  all  used  up  in  the  work  done  in 
bending  the  cord.  Such  a  traveling  loop  is  called  a  Wave. 
Notice  that  the  wave  travels  in  one  direction  along  one  side 
of  the  cord,  and  that  when  it  is  reflected  at  the  end  of  the 
cord  it  travels  back  along  the  opposite  side. 

Since  the  particles  of  the  cord  vibrate  at  right  angles  to 
the  length  of  the  cord  and  hence  to  the  direction  of  motion 
of  the  wave,  such  a  wave  is  called  a  wave  of  transverse 
vibration. 

Stretch  the  cord  and  hold  it  tightly  with  one  hand  about 
six  inches  from  the  free  end.  With  the  other  hand  pull  the 
free  end  of  the  cord,  stretching  the  part  between  the  hands, 
and  let  it  fly  back  with  a  snap.  Observe  the  pulse  that  is 
set  up  in  the  cord.  Make  one  that  will  travel  several  times 
the  length  of  the  cord  before  it  comes  to  rest. 

If  the  cord  was  properly  held  in  the  last  experiment,  no 
sidewise  vibration  was  observed.  The  stretched  end  of  the 
cord  when  it  shortened  after  being  released  compressed  the 
coils  of  the  wire  immediately  in  front  of  it,  these  (in  separat- 
ing) compressed  other  coils  in  front  of  them,  and  thus  a 
pulse  or  wave  of  compression  was  sent  along  the  wire.  Since 
the  vibrations  of  the  wire  were  forward  and  back  in  the 
direction  of  propagation  of  the  wave,  this  wave  is  called  a 
wave  of  longitudinal  vibration,  or  a  compressional  wave.  It 
will  be  seen  at  once  that  a  wave  of  longitudinal  vibration 
must  cause  a  compression  or  expansion  of  the  body  by  which 
it  is  transmitted. 

Two  Forms  of  Wave-motion. — These  are  the  two 
forms  of  wave-motion  usually  distinguished.  In  one 
form  the  particles  of  the  vibrating  body  are  displaced 
sidewise  and  back  across  the  path  of  the  wave,  in  the 
other  they  are  pressed  together  and  then  expand  in  the 
direction  of  motion  of  the  wave.  Since  in  expanding 
they  do  not  stop  when  the  position  of  normal  equi- 


•  WAl/E-MOTION  AND  SOUND  205 

librium  has  been  reached,  the  compressed  part  of  the 
wave  is  regularly  followed  by  an  expanded  part. 

What  name  do  we  give  to  the  force  which  causes 
the  coils  of  wire  to  return  to  their  original  position  after 
they  are  stretched  or  bent  ? 

By  means  of  what  force  may  the  wave  be  said  to  be 
propagated  along  the  wire  ? 

Why  are  wood  and  glass  better  conductors  of  vibra- 
tions than  soft  rubber  ? 

What  kind  of  elasticity  is  found  in  fluid  bodies  ? 
What  kind  of  waves  would  you  expect  such  bodies  to 
transmit  ?  * 

The  Wave  Machine. 

LABORATORY  EXERCISE  67. — An  efficient  wave  machine 
may  be  constructed  as  follows :  Into  a  bar  of  wood  about 
ten  feet  long  drive  double-pointed  carpet  tacks  along  one 
side  at  regular  intervals  of  about  four  inches.  Procure  a 
long,  fine  copper  wire  (a  waxed  thread  may  be  used,  but 
becomes  more  easily  tangled  than  the  wire)  and  pass  it 
through  between  the  tacks  and  the  bar,  stringing  a  large 
brass  button  or  a  small  lead  weight  f  upon  it  between  each 
pair  of  tacks  and  using  a  heavy  iron  or  lead  ball  in  place  of 
the  button  at  one  end  of  the  series.  Allow  the  wires  with 
the  suspended  buttons  to  hang  down  about  two  feet  below 
the  bar,  as  shown  at  a  in  Fig.  59.  After  the  buttons  have 
all  been  adjusted  to  the  same  height,  tie  pieces  of  thread 
around  each  pair  of  wires  between  adjacent  buttons,  and 

*  An  exception  to  this  law  is  apparently  seen  in  the  most  familiar  form 
of  waves,  viz.,  the  waves  on  the  surface  of  water.  This  apparent  ex- 
ception disappears  when  it  is  remembered  that  these  water  waves  are 
not  transmitted  by  the  elasticity  of  the  water,  but  by  gravitation.  The 
top  of  the  wave  is  not  pulled  down  by  elasticity,  but  by  gravitation,  and 
the  energy  of  the  wave  is  like  the  energy  of  the  gravitation  pendulum. 

f  Weights  suitable  for  the  wave  machine  may  be  cut  from  a  piece  of 
small  lead  pipe  and  strung  upon  the  wire.  If  very  fine  wire  is  used, 
they  should  not  weigh  more  than  about  5  grams,  and  should  all  be  of 
the  same  weight. 


2O6 


PHYSICS 


draw  the  wires  together  as  shown  in  b  in  the  figure.     Slip 
the  thread  loops  down  to  the  same  height  on  all  the  wires. 


V 

V 

V 

V 

\ 

1 

FIG.  59. 

Set  the  heavy  ball  in  motion,  and  observe  the  passage  of  the 
wave  along  the  line  of  buttons.* 

Set  up  a  wave  of  transverse  vibration  in  the  wave  machine. 
A  wave  of  longitudinal  vibration. 

By  what  means  is  the  vibration  transmitted  from  one 
button  to  the  next  one  ? 

Could  you  set  up  a  wave  of  transverse  vibration  in  a  row 
of  disconnected  pendulums  ? 

Could  you  set  up  a  longitudinal  wave  in  such  a  row  of 
pendulums  if  they  were  not  allowed  to  strike  each  other  in 
their  swings  ? 

When  a  row  of  "collision  balls"  such  as  were  used  in 
Exercise  18  are  all  of  the  same  mass  and  are  hung  in  a  line 
touching  each  other,  if  a  ball  at  one  end  be  pulled  away  from 
the  others  and  allowed  to  swing  against  the  one  next  to  it, 
the  ball  at  the  farther  end  of  the  line  may  be  set  in  motion 
while  the  intervening  balls  apparently  remain  at  rest.  Does 
a  compressional  wave  pass  through  the  line  of  balls  ?  If  so, 
explain  how. 

Wave-front. — When  a  wave-motion  passes  along  a 
line,  the  wave-front  is  a  point  in  the  line.  If  a  wave- 
motion  passes  through  a  plane,  the  wave-front  is  a  line 

*  The  vibration  period  of  these  waves  may  be  varied  by  any  desired 
amount  by  clamping  the  wire  of  the  heavy  pendulum  so  as  to  change  its 
vibrating  length,  or  by  giving  it  forced  vibrations  with  the  hand. 


AND  SOUND  207 

of  the  plane.  When  a  wave-motion  passes  through  a 
medium  having  three  dimensions,  the  wave-front  is 
always  a  surface.  When  a  wave  passes  along  the 
spring  cord,  for  example,  the  wave-front  is  a  cross- 
section  of  the  cord. 

When  a  wave  is  set  up  within  an  isotropic  substance, 
since  the  properties  of  the  substance  are  the  same  in 
all  directions  the  wave  will  spread  out  in  all  directions 
with  equal  velocities,  hence  the  wave-front  will  be  the 
surface  of  a  constantly  enlarging  sphere. 

Wave-train. — We  have  thus  far  considered  but  one 
wave  at  a  time.  If  the  wave  under  consideration  be 
produced  by  a  periodically  vibrating  body,  as  a  tuning 
fork,  it  will  be  followed  at  equal  distances  by  other 
waves  of  the  same  kind  which  will  all  travel  at  the 
same  rate.  Such  a  series  of  successive  waves  is  called 
a  Wave-train. 

If  the  vibrations  of  the  body  producing  the  waves  do 
not  occur  at  regular  intervals,  its  vibration  is  said  to  be 
aperiodic,  and  its  waves  do  not  follow  each  other  at 
regular  distances  and  hence  do  not  constitute  a  wave- 
train. 

In  sound  waves  we  generally  have  to  deal  with 
wave-trains. 

Wave-length. — In  wave-trains,  the  wave-length  is 
the  distance  between  two  successive  wave-fronts,  or, 
what  is  the  same  thing,  the  distance  between  the  corre- 
sponding parts  of  two  successive  waves.  In  water 
waves,  the  elevated  part  of  the  wave  is  called  the  crest, 
and  the  sunken  part  is  called  the  trough.  A  wave- 
front  is  a  continuous  crest  or  a  continuous  trough,  and 
a  wave-length  is  the  distance  from  one  crest  or  trough 
to  the  next  one. 


2o8  PHYSICS 

Relation  of  Wave-length  to  Velocity  of  Propaga- 
tion.— If  a  wave-train  be  produced  by  a  body  having 
a  constant  period  of  vibration,  the  wave-length  will 
vary  as  the  velocity  with  which  the  waves  travel  through 
the  conducting  medium.  It  will  be  the  distance  which 
one  wave  travels  before  the  next  wave  is  produced.  If 
the  wave  velocity  should  be  doubled,  the  wave-length 
would  also  be  doubled. 

Relation  of  Wave-length  to  Period  of  Vibration. — 
The  wave-length  of  a  train  of  waves  in  a  given  sub- 
stance will  vary  directly  as  the  period  of  vibration  of 
the  body  by  which  they  are  caused.  Thus  if  the 
velocity  of  a  wave-train  be  one  thousand  feet  a  second, 
a  tuning  fork  vibrating  one  hundred  times  a  second  will 
produce  waves  ten  feet  long,  and  one  vibrating  two 
hundred  times  a  second  will  produce  waves  five  feet 
long.  The  longer  the  vibration  period  of  the  fork,  and 
accordingly  the  fewer  its  number  of  vibrations  a  second, 
the  longer  the  waves  in  its  wave-train. 

Let  v  =  the  velocity  of  wave  propagation,  n  =  the 
number  of  vibrations  a  second  of  the  inducing  body, 
and  A*  —  the  wave-length,  and  give  an  expression  for 
v  in  terms  of  n  and  A. 

Wave  Amplitude. — The  greatest  displacement  of  a 
vibrating  particle  in  a  wave  from  its  normal  position  of 
rest  is  called  the  Amplitude  of  the  wave.  The  ampli- 
tude of  a  water  wave  is  the  vertical  distance  from  the 
water  level  to  the  crest  or  trough  of  the  wave. 

Wave  Induction. — We  have  seen  that  the  energy  of 
a  vibrating  body  may  be  transmitted  in  the  form  of 
waves  by  any  elastic  medium  with  which  it  comes  in 
contact.  When  this  occurs,  the  waves  in  the  trans- 

*  The  Greek  letter  lambda. 


WA1/E-MOTION  AND  SOUND  209 

mitting  medium  are  said  to  be  induced  by  the  vibrating 
body.  These  waves  may  in  turn  induce  vibrations  in 
some  other  elastic  body  at  a  distance  from  their  origi- 
nal source. 

Induced  vibrations  are  of  two  classes,  Sympathetic 
or  Resonant  Vibrations  and  Forced  Vibrations.  In 
the  one  case  the  body  is  set  vibrating  in  its  natural 
period  by  a  series  of  properly  timed  impulses,  and  in 
the  other  case  it  is  forced  into  vibrations  of  an  un- 
natural period. 

Resonance. 

LABORATORY  EXERCISE  68. — (a)  Suspend  a  heavy  weight, 
as  a  pail  of  sand,  by  a  strong  cord  so  that  it  may  swing  as  a 
pendulum.  Then  by  means  of  a  series  of  slight  impulses 
applied  just  as  you  would  apply  them  to  a  person  in  a  swing, 
set  the  heavy  pendulum  in  vibration.  In  this  case,  the  total 
energy  of  the  vibrating  pendulum  is  nearly  the  sum  of  all  the 
quantities  of  energy  given  to  it  by  the  original  impulses. 

Can  you  produce  the  same  effect  by  impulses  applied 
slower  or  faster  than  the  ones  previously  used  ?  Why  ? 

(b)  Explain  how  the  waves  sent  off  by  one  tuning  fork  can 
set  another  tuning  fork  in  vibration. 

What  is  necessarily  true  of  the  vibration  periods  of  the 
two  forks  ? 

(c)  Take   a  glass  tube  about   30  centimeters    long  and 
about  2  or  3  centimeters  in  internal  diameter  and  stand  it 
upright  in  a  tall  cylinder  or  other  deep  vessel  of  water  as 
in  Fig.  60.      Hold  a  sounding  tuning  fork  with  the  side  of 
one  prong  directly  above  the  open  end  of  the  tube,  and  raise 
or  lower  the  tube  in  the  water  until  the  column  of  air  in  the 
tube  sounds  loudly  in  unison  with  the  fork.      Such  a  tube 
is  called  a  Resonance  Tube. 

What  reason  have  you  for  thinking  that  the  air  column  is 
in  vibration  ? 

Why  will  not  a  longer  or  a  shorter  column  of  air  vibrate 
as  well  ? 

Repeat  the  experiment  with  another  fork  having  a  different 
vibration  period.  Are  the  vibrating  air  columns  of  the  same 
length  for  the  two  forks  ? 


2IO 


PHYSICS 


(d)  Hold   a   vibrating  tuning  fork   to  the  mouth  of  an 
organ  pipe  which  gives  the  same  note  as  the  fork.     Is  the 
organ  pipe  also  a  resonance  tube  ? 

(e)  Take  a  wide-mouthed  glass  vessel,  as  a  fruit  jar  or  a 


FIG.  60. 


tumbler,  and  cover  its  mouth  with  a  piece  of  glass  or  heavy 
cardboard,  leaving  only  a  narrow  opening  at  one  side  of  the 
vessel.  Hold  a  vibrating  tuning  fork  above  this  opening  and 
adjust  the  width  of  the  opening  by  sliding  the  cover  of  the 
vessel  until  you  find  a  position  where  the  enclosed  air  will 


WAPE-MOTION  AND  SOUND  211 

vibrate  in  unison  with  the  fork.  Such  a  vessel  is  called  a 
Resonator. 

Does  the  same  resonator  resound  equally  well  to  forks  of 
different  vibration  period  ? 

Does  the  enclosed  air  in  the  resonator  have  a  natural  period 
of  vibration,  as  a  pendulum  does  ? 

To  show  the  vibrations  of  the  air,  stick  the  cover  in  place 
with  wax,  and  then  stretch  a  soap  film  over  the  opening  by 
inverting  the  resonator  in  a  soap  solution,  or  by  spreading 
the  film  over  the  opening  by  means  of  a  soft  brush.  Then 
hold  the  vibrating  tuning  fork  so  that  the  resonator  will 
resound  to  it  and  observe  the  soap  film  over  the  opening. 

A  permanent  resonator  may  be  made  by  pasting  a  piece 
of  wet  linen  paper  over  the  mouth  of  a  jar  or  tumbler  and 
allowing  it  to  dry,  then  cutting  an  opening  in  the  paper  at 
one  side  of  the  jar  and  enlarging  it  until  the  resonator  is 
properly  tuned.  The  size  of  the  opening  should  be  deter- 
mined beforehand  by  use  of  a  glass  or  cardboard  cover. 

When  such  a  resonator  resounds  to  a  fork,  the  vibrations 
may  be  shown  by  scattering  sand  on  the  paper  and  inclining 
the  resonator  so  that  the  sand  will  nearly  slide  off  when  the 
paper  is  at  rest.  Then  when  the  paper  vibrates  the  sand  will 
slide  down  the  incline. 

(/)  Hold  a  vibrating  tuning  fork  in  front  of  your  mouth 
and  try  to  adjust  the  mouth  cavity  so  that  it  will  serve  as  a 
resonator  for  the  fork. 

The  cavity  of  the  external  ear  serves  as  a  resonator 
for  certain  very  shrill  sounds,  and  for  this  reason  these 
sounds  seem  very  loud  and  sometimes  become  painful. 
It  is  for  this  reason  that  the  sounds  of  some  insects,  as 
the  chirping  of  a  cricket,  are  heard  so  plainly. 

Forced  Vibrations. — If  a  string  be  tied  to  the  heavy 
pendulum  used  in  the  preceding  exercise,  the  pendulum 
may  be  made  to  swing  faster  or  slower  than  its  normal 
rate  by  pulling  on  the  string.  The  pendulum  is  then 
said  to  make  forced  vibrations. 

When  the  stem  of  a  vibrating  tuning  fork  is  held 
against  a  board,  the  surface  of  the  board  is  forced  into 


212  PHYSICS 

vibrations  of  the  same  period  as  the  vibrations  of  the 
fork.  Thus  the  same  board  can  be  made  to  vibrate  to 
any  fork.  When  tuning  forks  are  mounted  on  boxes 
to  reinforce  their  sound,  a  box  is  usually  chosen  which 
is  a  resonator  for  the  particular  fork  which  is  to  be 
mounted  upon  it.  The  sound  of  the  fork  is  then 
reinforced  by  the  forced  vibrations  of  the  sides  of  the 
box  and  the  sympathetic  vibrations  of  the  enclosed  air. 

The  vibrations  of  the  sounding  boards  of  musical 
instruments,  as  the  piano,  the  violin,  and  the  guitar, 
are  forced  vibrations.  The  vibrations  of  the  air 
columns  in  wind  instruments  are  sympathetic  vibrations. 
The  sounds  of  the  voice  in  speaking  or  singing  are 
caused  by  sympathetic  vibrations,  and  their  vibration 
period  is  changed  by  changing  the  shape  of  the  reso- 
nating cavities  of  the  mouth  and  pharynx  or  by  vary- 
ing the  size  of  their  openings  into  the  external  air. 

Reflection  of  Waves. — In  the  experiments  with  the 
brass  spring-cord,  you  saw  that  a  wave  traveling  along 
the  cord  is  reflected  at  the  fixed  end  and  travels  back 
along  the  opposite  side  of  the  cord.  Since  only  a  part 
of  the  energy  of  the  wave  could  be  given  off  to  the 
support  at  the  fixed  end  of  the  cord,  the  rest  traveled 
back  in  the  form  of  a  new  wave. 

The  same  phenomenon  may  be  observed  in  the  wave 
machine  by  sending  a  single  wave  along  the  row  of 
buttons.  The  end  button  cannot  give  off  its  energy  to 
any  other  body,  so  it  swings  back  to  the  other  side  of 
its  arc  and  thus  starts  a  wave  in  the  opposite  direction 
along  the  connected  row  of  buttons. 

The  reflection  of  sound  waves  is  also  a  well-known 
phenomenon,  and  gives  rise  to  echoes.  When  a  sound 
wave  traveling  through  the  air  meets  an  obstruction. 


WAVE-MOTION  AND  SOUND  213 

part  of  its  energy  is  given  to  the  obstruction  and  the 
rest  is  turned  back  as  a  reflected  wave. 

Interference  of  Waves  by  Reflection. — When  ad- 
vancing and  reflected  wave-trains  are  traveling  through 
the  same  medium  they  often  interfere  with  each  other's 
vibrations  and  produce  new  phenomena.  One  of  the 
commonest  effects  of  interference  by  reflection  is  the 
production  of  standing  waves. 

Standing  Waves. 

LABORATORY  EXERCISE  69. — Set  the  heavy  pendulum  of  the 
wave  machine  swinging  and  observe  the  wave-train  produced 
as  it  passes  along  the  row  of  buttons  and  returns  after  reflec- 
tion. You  will  see  that  at  certain  points  along  the  line  the 
advancing  and  reflected  waves  meet,  and  that  the  successive 
waves  of  the  two  trains  meet  at  the  same  points.  At  these 
points  the  pendulums  tend  to  swing  under  the  influence  of 
two  equal  and  opposite  impulses,  and  the  result  is  that  they 
do  not  swing  in  either  direction.  You  will  probably  be  able 
to  observe  several  of  the  pendulums  which  are  practically  at 
rest  while  those  on  either  side  of  them  are  in  full  vibration. 
The  waves  produced  by  the  inducing  pendulum  accordingly 
appear  to  stand  still  and  cause  the  same  pendulums  to 
vibrate  all  the  time,  hence  they  are  called  standing  waves. 

Take  the  free  end  of  the  spring-cord  in  the  hand  and  start 
a  transverse  wave  along  it.  Just  at  the  instant  when  this 
wave  is  being  reflected,  start  another  to  meet  it.  If  properly 
timed,  they  will  meet  and  pass  each  other  at  the  middle  of 
the  cord,  and  this  part  of  the  cord  will  remain  at  rest  while 
they  are  passing. 

Swing  the  end  of  the  cord  back  and  forth  so  that  it  will 
vibrate  in  two  parts  with  a  place  of  no  vibration  between 
them.  Cause  it  to  vibrate  in  three  parts.  In  four  parts. 

When  the  vibrations  are  properly  timed,  the  advancing 
and  reflected  wave-trains  always  meet  at  the  same  places  and 
the  cord  vibrates  in  standing  waves. 

Standing  waves  as  distinguished  from  moving  waves  have 
certain  fixed  parts.  In  a  moving  wave,  every  particle  which 
takes  part  in  the  wave-motion  goes  through  the  same  series 
of  vibrations  as  the  other  particles  of  the  wave  and  there  are 

,,THEH?\ 

NlVERSlTY  1 


214 


PHYSICS 


no  places  of  rest  and  no  parts  of  greatest  vibration.  In 
standing  waves,  some  parts  of  the  cord  do  not  move  at  all. 

The  places  of  rest  in  a  standing  wave  are  called  Nodes. 
The  places  of  greatest  vibration  are  midway  between  the 
nodes,  and  are  called  Loops. 

The  wave-length  of  a  standing  wave  is  taken  as  the  dis- 
tance between  the  parts  of  two  adjacent  waves  which  are  in 
the  same  phase  of  vibration.  Since  successive  loops  are 
always  in  opposite  phases  of  vibration,  a  complete  wave- 
length always  takes  in  two  loops  and  two  nodes. 


FIG,  61. 

Fig.  6 1  shows  the  form  taken  at  a  particular  instant  by  the 
vibrating  cord  when  it  is  thrown  into  standing  waves.  The 
nodes  are  lettered  a,  b,  c,  and  d,  and  the  loops  A,  B,  and  C. 
A  wave-length  is  the  distance  from  A  to  C  or  from  a  to  c,  or 
from  b  to  d. 

We  are  now  ready  to  explain  the  peculiar  forms  taken 
by  the  cork  dust  in  the  vibrating  tube  used  in  Exercise 
64.  The  longitudinal  vibrations  of  the  tube  caused  the 
cork  in  one  end  to  set  up  waves  in  the  enclosed  air. 
These  waves  were  reflected  at  the  open  end  of  the  tube, 
just  as  the  weaves  are  reflected  from  the  free  end  of  the 
wave  machine,  and  in  returning  along  the  tube  set  up 
a  row  of  standing  waves  in  the  air  in  the  tube.  The 
cork  dust  is  set  in  motion  by  the  vibrations  of  these  air 
waves.  The  places  where  the  cork  dust  remains  at 
rest  are  the  nodes,  and  the  places  where  it  is  most 
violently  agitated  are  the  loops  of  these  waves.  Thus 
a,  b,  and  c  in  Fig.  62  are  nodes. 

The  wave-length  of  these  particular  sound  waves  in 


WAVE-MOTION  AND  SOUND 


215 


air  is  the  length  of  two  of  the  cork-dust  segments,  best 
measured  from  one  node  to  the  second  one  on  either 
side  of  it,  as  from  a  to  c. 


FIG.  62. 

Measure  a  number  of  the  segments  and  see  if  they  are  of 
uniform  length. 

If  the  velocity  of  these  sound  waves  is  338  meters  a  second, 
what  is  the  vibration  period  of  the  cork  in  the  end  of  the 
tube  ? 

Interference  of  Sound  Waves. 

LABORATORY  EXERCISE  70. — We  have  seen  that  standing 
waves  may  be  produced  in  elastic  bodies  by  the  meeting  of 
similar  wave-trains  going  in  opposite  directions.  In  the 
case  of  the  glass  tube,  we  saw  these  standing  waves  produced 
by  the  meeting  of  trains  of  sound  waves  in  air.  We  now 
wish  to  study  some  of  the  other  phenomena  of  the  interfer- 
ence of  sound  waves. 

(a)  Sound  a  tuning  fork,  and  holding  the  side  of  the 
prongs  near  the  ear  rotate  the  stem  of  the  fork  in  the  fingers. 
As  the  fork  turns  around,  you  will  notice  that  when  the 
corner  of  its  nearest  prong  is  turned  toward  the  ear  the  sound 
of  the  fork  cannot  be  heard,  but  that  when  the  sides  or  the 
edges  of  the  prongs  are  turned  toward  the  ear  the  sound 
becomes  very  plain. 

The  explanation  of  this  phenomenon  is  as  follows:  When 
the  fork  sounds,  its  prongs  vibrate  always  in  opposite  direc- 


216  PHYSICS 

tions.  This  may  be  readily  shown  by  making  a  tracing  on 
smoked  glass  by  means  of  little  points  attached  to  the  ends 
of  the  prongs  of  a  vibrating  fork.  Fig.  63  is  photographed 


FIG.  63. 

from  such  a  tracing.  As  the  prongs  separate  they  drive 
away  the  air  on  the  outer  side  of  both,  while  the  air  near 
their  edges  rushes  into  the  enlarged  space  between  them. 
When  the  prongs  approach  each  other,  the  air  between  them 
is  compressed  and  forced  outwards,  while  the  air  on  the 
outer  sides  of  the  prongs  follows  them  inward  toward  the 
center. 

This  condition  is  represented  in  Fig.  64,  where  you  are 
supposed  to  be  looking  directly  toward  the  ends  of  the 
prongs.  The  arcs  of  the  circles  shown  in  dotted  lines  are  to 
represent  the  region  in  which  the  air  is  vibrating  toward  the 
fork,  and  the  arcs  shown  in  entire  lines  represent  the  regions 
where  the  air  is  vibrating  away  from  the  fork.  In  each 
region  a  wave-train  is  set  up  with  alternate  vibrations  toward 
and  from  the  fork,  but  where  these  wave-trains  meet  along 
lines  drawn  out  from  the  corners  of  the  fork  their  vibrations 
are  always  in  opposite  directions  and  neutralize  each  other. 
Along  these  lines  there  are  accordingly  no  waves,  but  the  air 
remains  at  rest-. 

(b)  Bow  the  Chladni's  Plate,  and  scatter  sand  upon  it  to 
show  the  lines  of  no  vibration  in  the  plate  The  plate  is 
seen  to  vibrate  in  standing  waves  and  the  sand  lines  represent 
the  nodes.  On  opposite  sides  of  the  sand  lines  the  segments 
of  the  plate  are  accordingly  vibrating  in  opposite  directions. 

Take  a  glass  funnel  of  about  three  inches  in  diameter  and 
slip  a  piece  of  rubber  tubing  of  convenient  length  over  its 


WAfE-MOTION  AND  SOUND 


217 


stem.  Hold  the  other  end  of  the  rubber  tubing  in  the  ear, 
and  move  the  mouth  of  the  funnel  about  over  the  vibrating 
plate  and  within  an  inch  or  so  of  its  surface.  When  the 
funnel  is  held  above  any  one  of  the  vibrating  segments  the 
sound  of  the  plate  is  plainly  heard  through  the  tube.  When 
it  is  held  above  a  node  so  that  as  many  waves  enter  it  from 


FIG.  64. 

one  side  of  the  node  as  from  the  other,  no  sound  is  heard. 
The  two  sets  of  waves  which  enter  the  funnel  tend  to  pro- 
duce vibrations  in  the  opposite  direction  at  the  same  time 
and  accordingly  no  vibration  is  produced.  The  two  sounds 
are  accordingly  said  to  destroy  each  other  by  interference. 

(c)  Prepare  two  resonators  from  two  similar  jars  or  wide- 
mouthed  bottles,  and  adjust  them  so  that  they  resound 
equally  well  to  the  same  fork.  Notice  that  either  resonator 
will  sound  to  the  sides  or  edges  of  the  fork  prongs,  but  not 
when  the  corner  of  the  prong  is  held  above  the  mouth  of  the 
resonator. 

Stand  one  resonator  upon  the  table  and  hold  the  vibrating 
fork  above  it  so  that  the  resonator  will  sound  to  the  side  of 
the  prongs,  Hold  the  other  resonator  in  the  hand  in  a  hori- 
zontal position  so  that  it  may  sound  to  the  edges  of  the 


2i8  PHYSICS 

prongs  at  the  same  time,  as  in  Fig.  65.  The  waves  which 
emerge  from  the  two  resonators  are  now  vibrating  in  opposite 
directions,  and  will  interfere  with  each  other.  Hold  the  fork 
and  resonator  in  such  positions  that  the  sounds  issuing  from 
the  two  resonators  may  entirely  destroy  each  other.  Prove 


FIG.  65. 

that  both  resonators  are  sounding  all  the  time  by  having 
another  person  cover  the  mouth  of  first  one  and  then  the 
other  with  a  card.* 

*  It  is  not  true,  strictly  speaking,  that  in  experiments  (/>)  and  (d]  the 
two  sound  waves  destroy  each  other.  The  energy  of  wave- motion  is  not 
decreased,  but  the  waves  produced  by  the  vibrating  plate  and  the  vibrat- 
ing tuning  fork  do  not  spread  out  as  before. 

In  the  case  of  the  plate,  since  the  segments  are  vibrating  in  opposite 
directions,  the  air  waves  in  the  two  halves  of  the  funnel  are  vibrating  in 
opposite  directions,  so  the  air  moves  up  one  side  of  the  funnel  and  down 
the  other  at  the  same  time,  and  the  air  in  the  stem  is  not  appreciably 
affected  by  this  motion. 

In  the  case  of  the  two  resonators,  the  air  rushes  out  of  one  and  into 
the  other  and  back  again,  and  almost  the  whole  energy  of  the  vibration 


WAVE-MOTION  AND  SOUND  219 

(d)  Hold  one  of  the  large  mounted  forks  in  the  hand  with 
the  mouth  of  its  resonance  box  toward  a  smooth  wall  and 
bow  the  fork  until  it  sounds  loudly.     Then  move  it  forward 
and  back,  toward  and  from  the  wall,  and  notice  the  places 
where  the  sound  of  the  fork  is  weakened.     These  places  are 
where  the  sound  waves  reflected  from  the  wall  interfere  with 
the  waves  which  the  fork  is  sending  off  away  from  the  wall. 
If  the  fork  is  at  such  a  distance  from  the  wall  that  the  waves 
which  travel  to  the  wall  and  back  are  vibrating  in  opposite 
phase  to  those  which  start  directly  from  the  fork,  the  two 
sets  of  waves  will  interfere  destructively  with  each  other.     If 
the  reflected  waves  fall  in  with  the  others  in  the  same  phase 
of  vibration,  the  two  sounds  will  strengthen  each  other. 

Since  the  two  halves  of  a  wave  are  always  in  opposite 
phases  of  vibration,  the  reflected  waves  will  interfere  with 
the  others  when  they  have  traveled  a  half  wave-length  farther, 
or  three  half  wave-lengths,  or  any  odd  number  of  half  wave- 
lengths farther  than  the  others.-  Since  the  reflected  waves 
travel  to  the  wall  and  back  again,  their  path  is  lengthened 
by  twice  the  distance  that  the  fork  is  moved  away  from  the 
wall.  There  ought  accordingly  to  be  a  place  of  destructive 
interference  for  every  half  wave-length  of  the  sound  of  the 
fork  as  the  fork  approaches  or  leaves  the  wall. 

Measure  in  this  way  the  wave-length  of  the  sound  given 
off  by  the  fork.  If  the  number  of  vibrations  a  second  of  the 
fork  is  known,  calculate  the  velocity  of  sound  in  air. 

Another  form  of  sound  interference  is  shown  in  the 
phenomenon  of  beats. 

(e)  Sound  together  the  two  forks  used  in  the  resonance 
experiment.      Note  that  their  sounds  blend  into  a  smooth 
note.     Slow  down  the  vibrations  of  one  fork  by  sticking  a 
small  weight,  as  a  coin,  to  one  of  its  prongs  by  means  of  a 
piece  of  wax,  and  sound  the  forks  together  by  bowing  them 
with  the  violin  bow.      Notice  that  their  sound  is  alternately 
strengthened  and  weakened,  as  in  the  case  of  the  fork  moved 
in  front  of  the  wall.      The  two  forks  are  now  said  to  beat 
with  each  other.      When  the  two  forks  have  the  same  vibra- 
is  confined  to  the  air  in  the  resonators.    .If  either  resonator  be  covered, 
the  air  wave  coming  out  of  the  other  cannot  rusli  into  it,  and  it  accord- 
ingly spreads  out  into  the  surrounding  air.     The  energy  of  vibration  is 
accordingly  as  great  when  the  resonators  are  placed  for  interference  as 
it  was  before. 


220  PHYSICS 

tion  period  and  are  sounded  together  they  adjust  themselves 
to  each  other  so  that  their  wave-trains  go  out  in  the  same 
phase  from  both.  When  the  period  of  the  two  is  slightly 
different,  their  wave-trains  meet  alternately  in  the  same  phase 
and  in  opposite  phase,  thus  alternately  strengthening  and 
weakening  each  other's  sound. 

If  one  fork  sends  off  one  wave  a  second  more  than  the 
other,  their  waves  will  meet  in  the  same  phase  once  a  second 
and  in  opposite  phase  once  a  second. 

Change  the  position  of  the  weight  on  the  prong,  and 
notice  the  change  in  the  number  of  beats. 

Adjust  the  forks  so  that  they  beat  two  or  three  times  a 
second  and  try  the  resonance  experiment  with  them.  Explain 
your  result. 

Beats  can  be  plainly  heard  in  the  wires  of  a  piano  by  rais- 
ing the  damper  and  striking  together  a  white  key  and  its 
adjacent  black  key. 

How  could  you  make  use  of  beats  in  tuning  two  wires  to 
the  same  vibration  period  ? 

When  a  church  bell  sounds,  it  vibrates  in  segments,  as 
the  Chladni's  Plate  or  the  bowed  glass  vessel  used  in  Exer- 
cise 64.  Usually  on  account  of  irregularities  in  the  thickness 
of  the  bell  the  segments  do  not  all  have  the  same  vibration 
period,  hence  they  produce  beats.  These  beats  can  be  most 
plainly  heard  when  the  sound  of  the  bell  is  dying  out. 

Velocity  of  Wave  Propagation. 

LABORATORY  EXERCISE  71. — Take  the  free  end  of  the  brass 
spring-cord  in  the  hand  and  send  a  wave  along  it,  holding 
the  cord  loosely  stretched.  Repeat,  stretching  the  cord 
tightly,  and  notice  the  difference  in  the  velocity  with  which 
the  two  waves  move  along  the  cord.  Start  a  wave  in  the 
loose  cord,  and  stretch  the  cord  while  the  wave  is  passing 
along  it. 

How  does  the  stretching  force  applied  to  the  cord  affect 
the  velocity  of  wave-motion  along  it  ? 

The  same  phenomenon  may  be  observed  in  standing  waves 
as  follows:  Fasten  a  fine  silk  thread  about  thirty  or  forty 
centimeters  long  by  means  of  a  piece  of  wax  to  one  prong 
of  a  large  mounted  tuning  fork.  Carry  the  thread  over  a 
convenient  support  and  attach  a  weight  to  the  end  to  keep 
the  thread  stretched.  Bow  the  fork  as  shown  in  Fig.  66, 


U/Al/E-MOTION  AND  SOUND 


221 


so  that  the  thread  may  vibrate  in  standing  waves.  Make  the 
weight  heavy  enough  to  cause  the  vibrating  segments  to  be 
four  or  five  centimeters  long,  and  place  the  support  so  that 


FIG.  66. 

there  may  be  two  segments  between  it  and  the  fork,  as 
shown  in  the  figure. 

Leaving  everything  else  in  position,  remove  the  suspended 
weight  and  replace  it  by  one  one-fourth  as  heavy,*  and  note 
the  length  of  the  standing  waves  when  the  fork  is  made  to 
vibrate. 

Replace  this  weight  on  the  thread  by  one  four  times  as 
heavy  as  the  first  weight,  and  note  the  wave-length  as  before. 

Tabulate  your  results  as  follows : 


Stretching 
Force. 

No.  of 
Waves. 

Wave- 
length. 

I 

4 

16 

*  Weights  of  lead  or  heavy  wire  for  this  experiment  should  be  pre- 
pared by  the  teacher.  Their  magnitude  will  depend  upon  the  rapidity  of 
vibration  of  the  fork  used. 

An  electrically  driven  fork  is  better  for  this  experiment  than  one 
bowed  by  hand,  but  the  experiment  as  described  offers  no  difficulties. 


222  PHYSICS 

How  does  the  number  of  waves  in  a  given  length  of  thread 
vary  with  the  stretching  force  ? 

How  does  the  wave-length  vary  with  the  stretching 
force  ? 

How  does  the  velocity  of  wave  propagation  in  a  stretched 
string  vary  with  the  stretching  force  ? 

In  these  experiments,  the  elasticity  by  means  of  which  the 
wave  is  propagated  is  measured  by  the  stretching  force  along 
the  cord,  since  this  is  the  force  under  which  the  cord 
vibrates.  We  can  accordingly  use  the  term  elasticity  of 
vibration  instead  of  stretching  force  in  the  equations  which 
express  the  results  of  our  experiments. 

Does  the  equation  v  oc  Vs,  where  v  represents  wave 
velocity  and  s  represents  the  elastic  force  which  causes  the 
vibration,  express  the  results  of  your  experiments  ? 

Leaving  the  apparatus  in  position,  replace  the  thread  by 
one  made  of  a  piece  off  the  same  spool  doubled  into  four 
strands  and  lightly  twisted.  Attach  the  heaviest  weight 
previously  used,  and  measure  the  length  of  the  waves  in  the 
heavy  thread. 

How  does  this  wave-length  compare  with  the  wave-length 
of  the  single  thread  stretched  by  the  same  force  ? 

Is  it  true  to  say  that  the  wave-length  is  decreased  as  the 
square  root  of  the  weight  of  the  thread  is  increased  ? 

I/stretching  force 
Does  the  equation,  velocity  oc  — ,  represent 

Vweight 
the  results  of  your  measurements  ? 

What  would  be  the  wave-length  in  the  single  thread 
if  the  stretching  force  were  25? 

What  would  be  the  wave  length  of  the  heavy  thread 
stretched  by  a  force  of  256  ? 


h» 


eneral  Equation  of  Wave-motion. — The  formula 
derived  in  the  preceding  experiments  for  the  velocity 
of  wave-motion  in  stretched  cords  applies  to  all  elastic 
bodies  by  letting  e  represent  the  modulus  of  elasticity 
of  the  body,  and  substituting  the  density  of  the  body 
for  the  weight  per  unit  length  of  the  cord.  Thus  the 


WA1SE-MOTION  AND  SOUND  223 

general  equation  for  wave-motion  in  an  elastic  medium 

V '  €  *  € 

is  v  = — -,  or,  as  it  is  frequently  written,  v2  =  — . 
Vd  d 

Water  has  a  density  of  one  and  an  elasticity  of  compression 
about  ten  thousand  times  that  of  air.  If  the  velocity  of 
sound  be  taken  as  338  meters  a  second  in  air,  what  should 
it  be  in  water  ? 

Relative  Velocity  of  Waves  in  Air  and  in  Glass. — 

In  the  experiment  with  the  glass  tube  and  the  cork 
filings,  the  waves  were  set  up  by  the  longitudinal  vibra- 
tions of  the  glass.  Since  the  tube  was  clamped  at  its 
center,  it  could  not  vibrate  as  a  whole,  but  could  only 
stretch  and  contract  like  a  piece  of  India  rubber,  though 
on  a  much  smaller  scale.  This  would  give  the  greatest 
vibration  at  the  ends  of  the  tube,  and  a  place  of  no 
vibration  at  its  center.  The  tube  would  accordingly 
vibrate  as  one  half  a  standing  wave,  having  a  node  at 
its  center  and  loops  at  its  ends.  The  vibration  period 
of  the  tube  is  accordingly  the  period  which  would  give 
standing  waves  in  glass  twice  as  long  as  the  tube. 

The  same  vibrations  produce  standing  waves  in  the 
air  in  the  tube.  The  wave-length  in  air  for  this  vibra- 
tion period  is  the  length  of  two  of  the  dust  segments  in 
the  tube.  One  of  the  cork-dust  segments  accordingly 
represents  half  a  wave-length  in  air  for  the  same  vibra- 
tion period  for  which  the  length  of  the  glass  tube  repre- 
sents half  a  wave-length  in  glass. 

Letting  v  stand  for  the  velocity  of  wave-motion  in 
air,  v'  for  the  velocity  in  glass,  /  for  the  length  of  a 
cork-dust  segment,  and  I'  for  the  length  of  the  tube, 
we  have  the  equation  v  :  v'  =  I :  I' . 

This  method  of  comparing  the  velocities  of  sound 


224  PHYSICS 

waves  was  invented  by  Prof.  Kundt,  and  the  apparatus 
is  known  as  Kundt 's  Tube. 

Measurement  of  Relative  Velocities  of  Waves  in 
Air  and  Glass. 

LABORATORY  EXERCISE  72. — Measure  the  relative  velocity 
of  a  sound  wave  in  air  and  in  glass. 

If  the  density  of  glass  is  2.6  and  the  density  of  air  .0013, 
how  great  is  the  elasticity  of  glass  as  compared  with  air  ? 

The  density  of  air  is  doubled  by  an  increase  of  pressure  of 
one  atmosphere;  how  much  would  the  density  of  glass  be 
increased  by  the  same  increase  of  pressure  ? 

The  velocity  of  wave-motion  in  other  solids  may  be  meas- 
ured by  using  a  rod  of  the  substance  clamped  in  the  middle 
and  carrying  a  disc  of  paper  or  cork  on  one  end,  and  insert- 
ing this  end  in  the  glass  tube  containing  the  cork  filings. 
When  the  rod  is  set  in  longitudinal  vibration,  the  disc  on  its 
end  sets  up  standing  waves  in  the  air  in  the  tube,  and  the 
length  of  these  waves  is  shown  by  the  cork  filings,  as  in  the 
preceding  experiment. 

NATURE    OF    SOUND 

Two  Definitions  of  Sound. — Thus  far  we  have  been 
concerned  chiefly  with  the  physical  side  of  Sound,  that 
is,  with  the  character  of  the  wave-motions  which  pro- 
duce the  sensation  of  Sound.  It  is  customary,  however, 
to  consider  also  in  a  text-book  on  Physics  some  of  the 
characteristics  of  the  sensations  produced  by  these 
vibrations. 

Classification  of  Sounds. — Sounds  are  usually  classi- 
fied as  musical  sounds  and  non-musical  sounds  or 
noises.  A  sound  which  is  produced  by  a  periodic 
vibration,  as  the  sound  of  a  tuning  fork  or  a  violin 
string,  gives  a  smooth,  pleasant  sensation,  and  is  called 
a  musical  sound.  One  which  is  produced  by  an 
aperiodic  vibration  is  called  a  noise.  Thus  the  vibra- 
tions which  produce  wave-trains  and  standing  waves 


U/AI/E-MOTION  AND  SOUND  225 

produce  musical  sounds,  while  those  which  produce 
irregular  waves  give  the  unpleasant  sensations  called 
noises. 

Limits  of  Audibility. — All  periodic  vibrations  do 
not  produce  musical  sounds.  When  the  siren  disc  is 
rotated  slowly,  the  puffs  of  air  blown  through  the  hole 
do  not  combine  to  form  a  continuous  sound.  The 
same  thing  is  true  in  the  case  of  a  card  held  against 
the  teeth  of  a  rotating  cog  wheel  or  the  spokes  of  a 
rotating  bicycle  wheel.  When  the  wheel  rotates  slowly, 
only  separate  taps  are  heard,  but  when  the  rotation  is 
sufficiently  rapid  these  taps  blend  into  a  continuous 
sound.  Experiments  have  shown  that  about  sixteen 
vibrations  a  second  are  as  few  as  can  be  combined  into 
a  continuous  sound.  Above  that  number,  the  sensa- 
tion of  sound  is  produced  by  vibrations  up  to  thirty 
thousand  or  more  a  second.  The  upper  limits  of  audi- 
bility vary  considerably  in  different  ears,  but  about 
thirty-four  thousand  a  second  is  considered  the  maxi- 
mum number  of  vibrations  which  can  produce  the 
sensation  of  sound  at  all.  To  greater  numbers  than 
these  our  ears  are  deaf,  and  it  is  not  improbable  that 
there  are  insects  which  communicate  with  each  other 
by  means  of  sounds  inaudible  to  the  human  ear.  Cer- 
tainly there  are  insects  whose  notes  are  above  the  limits 
of  audibility  of  some  ears,  but  which  can  be  heard  by 
others. 

MUSICAL   SOUNDS 

Properties  of  Musical  Sounds. — Musical  sounds  differ 
from  each  other  in  respect  to  their  Intensity,  their 
Pitch,  and  their  Quality. 

Intensity. — The  Intensity  or  Loudness  of  a  sound 
depends  upon  both  the  amplitude  of  vibration  and  the 


226  PHYSICS 

surface  of  vibration  of  the  inducing  body.  Thus  in  a 
given  tuning  fork  the  loudness  of  the  sound  depends 
upon  the  amplitude  of  vibration  of  the  prongs.  When 
the  prongs  have  nearly  come  to  rest,  the  sound  is  very 
feeble.  When  the  stem  of  the  fork  is  pressed  against 
the  table  the  sound  becomes  louder,  not  because  the 
amplitude  of  the  vibrations  of  the  table  are  greater  than 
those  of  the  fork,  but  because  the  vibrating  surface  of 
the  table  gives  its  own  amplitude  of  vibration  to  a  large 
quantity  of  air  in  contact  with  it,  while  the  tuning  fork 
disturbs  only  a  very  small  quantity  of  air.  When  the 
energy  given  to  the  air  by  each  is  distributed  through- 
out the  surrounding  air,  the  energy  of  vibration  due  to 
the  table  is  much  greater  at  any  particular  point  than 
that  due  to  the  fork. 

The  intensity  of  a  sound,  in  the  physical  sense,  is 
proportional  to  the  energy  of  the  sound  wave.  The 
energy  of  vibration  varies  as  the  square  of  the  velocity 
of  the  vibrating  body.  If  the  vibrations  are  made  in 
the  same  time  through  a  long  and  a  short  arc,  then  the 
velocity  of  vibration  is  proportional  to  the  amplitude  of 
vibration.  Thus,  if  a  pendulum  vibrates  in  the  same 
time  through  an  arc  two  centimeters  long  and  an  arc 
one  centimeter  long,  its  velocity  of  vibration  is  twice 
as  great  in  the  one  case  as  in  the  other,  and  its  energy 
of  vibration  is  four  times  as  great  in  the  one  case  as  in 
the  other. 

Intensity  and  Loudness. — The  loudness  of  a  sound 
has  reference  to  the  sensation  produced  by  the  sound, 
and  it  is  not  known  just  how  this  varies  with  the 
intensity  of  the  vibrations  entering  the  ear.  In  general, 
shrill  sounds  seem  louder  in  proportion  to  their  physical 
intensity  than  do  grave  sounds. 


WAVE-MOTION  AND  SOUND  227 

Variation  of  Intensity  with  Distance  from  Source. 

— The  intensity  of  a  given  sound  wave  at  a  distance 
from  its  source  must  depend  upon  the  area  of  the  sur- 
face to  which  its  energy  is  distributed.  Since  in  an 
isotropic  medium  the  sound  waves  spread  out  with 
equal  velocity  in  all  directions,  giving  spherical  wave- 
fronts,  the  intensity  of  a  given  sound  wave  at  any  point 
must  depend  upon  the  area  of  its  spherical  wave-front 
at  that  distance  from  its  source.  Since  the  area  of  the 
surface  of  a  sphere  increases  as  the  square  of  its  radius, 
the  intensity  of  a  sound  wave  in  an  isotropic  medium 
must  vary  inversely  as  the  square  of  the  distance  from 
its  source. 

When  a  wave  travels  along  the  spring-cord,  its 
intensity  decreases  very  slowly  with  the  distance  from 
the  source,  since  it  is  all  the  time  distributed  to  the 
same  length  of  cord,  and  its  energy  decreases  only  as 
it  is  used  up  in  heating  the  cord  or  is  given  off  to  the 
air  or  the  support  to  which  the  cord  is  attached.  This 
explains  how  sound  may  be  transmitted  so  far  by  the 
string  telephone. 

In  the  same  way,  a  wave  set  up  in  an  isolated  column 
of  air  loses  its  intensity  very  slowly,  hence  the  use  of 
speaking  tubes. 

Pitch. — The  pitch  of  a  musical  sound  depends  upon 
the  rapidity  of  the  vibrations  which  enter  the  ear.  If 
the  siren  disc  be  rotated  rapidly  while  it  is  sounding, 
its  note  becomes  higher  in  pitch  than  when  the  disc  is 
rotated  slowly.  The  same  thing  is  true  of  a  card  held 
against  the  spokes  of  a  rotating  wheel,  or  of  any  other 
vibrating  body  with  variable  period. 

Doppler's  Principle. 

LABORATORY  EXERCISE  73. — That    the  pitch  of  a  sound 


228  PHYSICS 

depends  upon  the  number  of  waves  entering  the  ear  in  a 
given  time  instead  of  upon  the  rapidity  of  vibration  of  the 
sounding  body  may  be  shown  as  follows : 

Slip  one  end  of  a  piece  of  rubber  tubing  about  a  meter 
long  over  the  mouthpiece  of  a  small  whistle,  so  that  the 
whistle  can  be  sounded  by  blowing  through  the  tube.  Let 
another  person  take  hold  of  the  tube  about  its  middle  and 
swing  the  whistle  around  in  a  vertical  circle  while  blowing 
through  the  tube.  Stand  so  that  the  whistle  alternately 
approaches  you  and  recedes  from  you,  and  listen  to  its  note. 
You  will  notice  that  the  pitch  of  the  tone  is  higher  while  the 
whistle  is  approaching  you  than  while  it  is  receding  from 
you.  In  the  one  case  a  greater  number  of  sound  waves  enter 
the  ear  in  a  given  time  than  in  the  other  case,  since  each 
wave  is  started  from  a  point  a  little  nearer  to  you  than  the 
previous  one,  and  the  waves  consequently  follow  each  other 
closer  together  than  if  the  whistle  were  at  rest.  If  the  sound 
waves  of  the  whistle  are  a  foot  long  and  the  whistle  advances 
an  inch  during  the  time  of  one  vibration,  the  waves  will  be 
induced  only  eleven  inches  apart  in  front  of  the  advancing 
whistle  and  thirteen  inches  apart  behind  it. 

The  same  difference  is  noticed  in  the  pitch  of  a  loco- 
motive whistle  when  the  train  is  approaching  you  and 
when  it  is  receding  from  you. 

This  dependence  of  the  apparent  pitch  of  a  note  upon 
the  motion  of  the  sounding  body  was  explained  by 
Doppler  in  1842,  and  is  known  as  Doppler's  Principle. 

Quality. — The  quality  of  a  tone  is  the  property  by 
virtue  of  which  we  distinguish  the  sounds  of  two  musical 
instruments,  as  a  flute  and  a  violin,  or  of  two  voices 
when  they  are  of  the  same  pitch  and  loudness. 

In  general,  musical  sounds  are  not  of  the  simple 
nature  of  those  produced  by  a  vibrating  tuning  fork, 
but  they  are  often  due  to  very  complex  vibrations. 

Relation  of  Quality  to  Complexity  of  Sound. 

LABORATORY  EXERCISE  74. — (a)  Blow  an  organ  pipe  in 
such  a  way  as  to  give  the  lowest  sound  of  which  the  instru- 


WAVE-MOTION  AND  SOUND  229 

ment  is  capable.  This  may  generally  be  done  by  blowing 
very  softly. 

Blow  harder  and  see  whether  you  can  produce  notes  of 
higher  pitch. 

Blow  so  that  two  or  more  notes  can  be  heard  in  the  pipe 
at  the  same  time. 

The  sounds  of  musical  instruments  and  the  sounds  of  the 
human  voice  are  usually  compound  sounds  in  which  two  or 
more  simple  musical  tones  can  be  heard.  One  of  these, 
usually  the  lowest,  is  louder  than  the  others  and  gives  the 
predominant  pitch  of  the  note. 

(b)  That  a  cord,   as  a  piano  wire  or  a  violin  string,   is 
capable  of  transmitting  two  or  more  trains  of  waves  at  the 
same  time  may  be  shown  by  setting  up  a  series  of  long, 
standing  waves   in  the  spring-cord,    and    then    by   several 
properly  timed  taps  on  the  vibrating  cord  setting  up  another 
series  of  shorter  waves  which  may  be  seen  running  over  the 
loops  of  the  longer  waves. 

All  wind  instruments  are  simply  resonators  in  which  the 
confined  air  columns  are  set  in  sympathetic  vibration.  We 
have  seen  that  a  resonator  may  be  tuned  for  any  period  of 
vibration,  but  we  have  not  seen  that  the  same  resonator  may 
have  more  than  one  natural  period  of  vibration.  This  is 
shown  as  follows: 

(c)  Place  the  glass  resonance  tube  used  in  Exercise  68  in 
its  cylinder  of  water,  hold  a  tuning  fork  above  it,  and  raise 
the  tube  in  the  water  until  it  resounds  to  the  fork.     Mark 
the  length  of  the  tube  above  the  water,  and  raise  it  until  you 
have  found  another  length  of  tube  which  resounds  to  the 
fork.     This  will  be  approximately  three  times  the  first  length. 

If  the  tube  is  long  enough,  find  a  third  length  of  tube  in 
which  the  air  resounds  to  the  fork.  If  the  cylinder  is  not  tall 
enough  for  this  experiment,  take  a  tube  about  a  meter  long 
and  measure  the  required  lengths  by  pushing  a  cork  along  in 
the  tube  instead  of  raising  and  lowering  the  tube  in  water. 

When  the  cork  is  properly  located  for  reinforcing  the 
sound  of  the  fork,  produce  a  note  from  the  tube  by  blowing 
across  its  open  end.  Do  you  get  a  different  note  for  every 
different  length  of  tube  ? 

When  is  the  note  induced  by  blowing  across  the  tube  the 
same  as  the  note  given  by  the  fork  ? 


2  3o  PHYSICS 

These  experiments  with  the  tube  show  that  standing 
waves  of  different  lengths  may  be  set  up  in  the  same  tube. 
The  number  of  waves  which  may  be  set  up  is,  however, 
limited  by  the  following  considerations: 

(a)  The  closed  end  of  the  tube  must  always  be  a  node, 
because  the  air  in  contact  with  this  end  is  not  free  to  vibrate. 

(/?)  The  open  end  of  the  tube  must  always  be  a  loop, 
since  here  is  the  place  where  there  is  greatest  freedom  of 
vibration. 

The  shortest  column  of  air  which  can  vibrate  to  a  tuning 
fork  in  a  tube  closed  at  one  end  is  accordingly  one  fourth 
the  wave-length  of  the  sound  in  air.  That  is,  the  tube  con- 
tains one  fourth  of  a  standing  wave,  with  a  node  at  the 
closed  end  of  the  tube  and  a  loop  at  the  open  end.  Accord- 
ingly, any  column  of  air  in  such  a  tube  can  vibrate  as  one 
fourth  of  a  standing  wave. 

The  next  longer  column  of  air  which  can  vibrate  to  the 
same  fork  is  one  in  which  there  is  a  node  at  the  closed  end, 
a  loop  at  the  open  end,  and  one  node  somewhere  in  the 
tube.  The  tube  will  then  be  three  fourths  of  a  wave-length 
of  the  sound  to  which  it  is  resounding. 

By  lengthening  the  tube  to  take  in  another  node,  it 
becomes  five  fourths  of  a  wave-length,  etc.  In  the  experi- 
ments with  the  Kundt's  Tube  you  saw  that  the  length  of  a 
tube  may  be  many  wave-lengths  of  the  standing  waves  set 
up  in  it. 

(d)  Cut  off  a  tube  of  the  same  diameter  as  the  one  you 
have  just  been  using  and  one  half  the  wave-length  of  the 
sound  of  your  fork.  The  tube  is  now  open  at  both  ends, 
and  should  be  capable  of  containing  one  half  of  a  standing 
wave  produced  by  the  fork,  but  must  have  a  loop  at  each 
end.  Since  you  can  have  half  a  wave-length  with  a  loop  at 
each  end,  the  tube  should  be  capable  of  resounding  to  your 
fork.  Will  it  do  so  ? 

This  tube  corresponds  to  the  Kundt's  Tube  clamped  at  its 
center,  except  that  in  this  case  the  sound  is  caused  by  the 
vibrating  air  column,  and  in  the  case  of  the  Kundt's  Tube  it 
was  caused  by  the  vibrating  tube  itself.  In  both  cases  there 
was  a  node  at  the  center  of  the  tube  and  a  loop  at  each  end. 

Complexity  of  the   Note  of  an  Organ  Pipe.— An 

organ  pipe  is  simply  a  resonance  tube  open  at  one  or 


W AYE-MOTION  AND  SOUND  231 

both  ends,  with  a  mouthpiece  so  arranged  that  in  blow- 
ing through  it  the  air  is  thrown  into  vibration  by  passing 
over  a  sharp  edge  of  wood  or  metal.  These  waves  are 
of  many  different  lengths.  If  any  of  them  are  of  suit- 
able length  for  setting  up  standing  waves  in  the  tube, 
they  will  do  so  and  the  tube  will  strengthen  the  sound 
of  their  particular  note.  The  harder  you  blow  into  the 
mouthpiece,  the  shorter  the  waves  you  produce,  and 
you  may  blow  so  hard  that  there  are  no  waves  capable 
of  setting  up  the  lowest  note  of  the  pipe.  In  this  case, 
the  pipe  may  strengthen  some  note  of  shorter  wave- 
length. 

In  general,  the  pipe  strengthens  more  or  less  all 
the  notes  which  are  capable  of  setting  up  standing 
waves  in  it,  hence  its  note  is  a  compound  note,  instead 
of  a  simple  note.  v£ 

Fundamentals  and  Overtones. — The  lowest  note 
which  a  resonator  of  any  kind  can  reinforce  is  called  its 
Fundamental.  The  higher  notes  are  called  Overtones. 
The  Quality  of  the  tone  depends  upon  the  relative 
loudness  of  the  fundamental  and  the  overtones. 

Overtones  in  a  Vibrating  Wire. 

LABORATORY  EXERCISE  75.- — Stretch  a  piano  wire  as  in 
Exercise  64  on  a  table  or  a  sounding  box,  and  cause  it  to 
sound  by  bowing  across  its  center.  In  this  way  you  set  up 
standing  waves  in  the  wire.  From  the  conditions  of  the 
experiment,  the  wire  has  a  node  at  each  end  and  a  loop  in 
the  middle.  It  is  accordingly  one  half  the  wave-length  of 
its  note.  The  wave-length  is,  however,  not  the  wave-length 
in  air,  but  the  wave-length  of  a  transverse  wave  of  that  par- 
ticular vibration  period  in  the  particular  wire  as  it  is  stretched 
in  the  experiment. 

Since  you  canot  make  the  wire  vibrate  as  less  than  half  a 
wave-length,  you  cannot  have  a  note  with  longer  waves  (and 
consequently  with  slower  vibrations)  than  the  one  already 


232  PHYSICS 

produced.  This  is  the  fundamental  note  of  the  wire  as  it  is 
stretched  for  the  experiment. 

Touch  the  wire  lightly  with  one  finger  exactly  at  its  middle 
point  while  you  bow  it  near  one  end.  You  will  be  able  in 
this  way  to  set  up  standing  waves  half  as  long  as  the  others, 
since  by  damping  the  center  of  the  wire  you  produce  a  node 
at  that  point. 

Prove  that  a  node  was  formed  where  the  finger  touched 
the  wire  by  hanging  on  the  wire  a  little  rider,  made  of  a 
narrow  strip  of  paper  or  a  bent  wire,  after  the  finger  has  been 
removed  and  while  the  wire  is  still  sounding. 

Since  the  weight  and  elasticity  of  the  wire  remain  the  same 
as  before,  the  velocity  of  wave  propagation  along  it  is 
unchanged.  Since  v  •=.  nX,  and  since  v  is  unchanged  and  A 
is  one  half  as  great  as  before,  what  change  has  taken  place 
in  n  ?  What  change  in  pitch  do  you  observe  to  correspond 
with  this  difference  in  vibration  period  ? 

Cause  the  wire  to  vibrate  in  three  segments  by  touching  it 
at  the  place  for  one  node  and  bowing  near  the  end,  as 
before.  Prove  by  the  use  of  riders  that  two  nodes  are 
formed.  How  does  the  number  of  vibrations  which  the  wire 
now  makes  in  a  second  compare  with  the  number  made  by 
its  fundamental  note  ? 

In  this  way  a  wire  may  be  made  to  vibrate  in  two,  three, 
four,  etc.,  segments,  giving  a  different  overtone  in  each  case. 
This  series  of  overtones  is  called  the  Harmonic  Series.  The 
first  harmonic  is  the  one  whose  vibration  number  is  twice 
that  of  the  fundamental;  the  second,  the  one  whose  vibration 
number  is  three  times  that  of  the  fundamental,  etc.  When 
a  violin  string  is  bowed  or  a  piano  wire  is  struck,  some  of 
these  overtones  are  always  produced  along  with  the  funda- 
mental. The  difference  in  the  tone  of  violins  is  due  to  the 
strengthening  of  different  overtones  by  the  sounding  board, 
or  by  the  resonance  of  the  air  in  the  box. 

Overtones  in  Organ  Pipes. 

Show  by  a  diagram  locating  the  nodes  and  loops  which 
overtones  of  the  harmonic  series  may  be  produced  in  an 
organ  pipe  open  at  both  ends.  In  an  organ  pipe  closed  at 
one  end. 

How  long  must  an  open  pipe  be  to  give  the  same  funda- 
mental note  as  a  closed  pipe  two  feet  long  ? 


WA^E-MOTION  AND  SOUND  233 

PHYSICAL    THEORY   OF    MUSIC 

Consonant  and  Dissonant  Tones. — It  has  long  been 
known  that  certain  tones  when  sounded  together  pro- 
duce a  pleasant  sensation,  while  others  produce  a  very 
unpleasant  sensation.  Two  tones  which  when  sounded 
together  blend  with  a  pleasant  sensation  are  said  to  be 
Consonant,  while  two  which  produce  an  unpleasant 
sensation  are  said  to  be  Dissonant.  On  account  of  this 
difference  in  the  blending  of  tones,  certain  combinations 
of  tones  have  been  chosen  for  musical  instruments  and 
for  singing,  while  other  combinations  are  carefully 
avoided. 

Cause  of  Dissonance. 

LABORATORY  EXERCISE  76. — The  physical  cause  of  dis- 
sonance was  first  discovered  by  Helmholtz,  and  may  be 
understood  from  the  following  exercise: 

Sound  together  the  two  tuning  forks  which  are  tuned  for 
resonance.  Weight  one  of  the  forks  so  as  to  give  several 
beats  a  second,  and  sound  both  forks  again.  By  increasing 
the  weight  on  the  one  fork,  increase  the  number  of  beats 
until  they  become  very  rapid,  and  observe  the  sensation  pro- 
duced in  your  ears  by  the  sound  of  the  two  forks. 

You  have  seen  that  as  the  number  of  beats  in  a  second 
increases  the  dissonance  of  the  two  sounds  increases.  When 
the  number  of  beats  becomes  as  great  as  thirty  or  forty  a 
second  the  dissonance  becomes  very  great.  Helmholtz  found 
that  the  maximum  discomfort  was  produced  by  the  two 
sounds  when  in  notes  of  medium  pitch  the  number  of  beats 
is  about  thirty-two  a  second.  Above  that  number  the  beats 
begin  to  coalesce  into  a  continuous  tone.  With  notes  of 
higher  pitch  the  maximum  dissonance  is  produced  when  the 
beats  are  still  more  rapid. 

It  follows  that  two  tones  whose  vibration  numbers  differ 
by  less  than  thirty  or  forty  vibrations  a  second  are  not  suit- 
able to  be  used  together  in  music. 

Dissonance   of   Compound  Tones. — We  have  seen 


234  PHYSICS 

that  most  musical  instruments,  as  well  as  the  human 
voice,  give  compound  tones,  and  if  their  overtones  are 
sufficiently  loud,  beats  between  them,  or  between  any 
of  them  and  the  fundamental  of  the  other,  may  cause 
dissonance.  This  limits  very  greatly  the  number  of 
tones  that  are  suitable  for  use  in  vocal  or  instrumental 
music. 

Musical  Scales. — Long  before  the  cause  of  dis- 
sonance was  understood  musicians  had  selected  a  series 
of  tones  bearing  certain  numerical  relations  to  each 
other  in  their  vibration  numbers,  and  known  as  a 
Musical  Scale.  These  tones  were  selected  because 
they  gave  less  dissonance  with  each  other  than  other 
tones  in  the  same  range  of  pitch. 

Musical  scales  have  been  developed  slowly  in  the 
history  of  the  race,  and  differ  in  different  countries  at 
the  present  time.  Certain  consonant  combinations 
were  recognized  in  very  early  times.  The  best  of  these 
was  a  note  and  its  first  harmonic  (now  called  its  octave, 
because  six  other  notes  are  introduced  between  them 
in  the  musical  scale).  When  these  two  notes  are 
sounded,  there  is  no  sound  in  the  higher  tone  not  also 
heard  in  the  other.  Thus  the  first  harmonic  of  the 
higher  note  is  the  third  harmonic  of  the  lower,  the 
second  harmonic  of  the  higher  is  the  sixth  of  the  lower, 
etc.  The  two  notes  accordingly  blend  so  as  to  pro- 
duce the  best  consonance  known. 

The  second  best  consonance  is  between  a  note  and 
the  fifth  of  its  octave,  that  is,  between  do  and  sol. 
Here  the  vibration  numbers  are  as  two  to  three.  In 
this  combination,  the  first  harmonic  of  the  upper  note 
becomes  the  second  of  the  lower  note,  the  third  of  the 
upper  becomes  the  fifth  of  the  lower,  etc. 


WAVE-MOTION  AND  SOUND .  235 

Musical  Instruments. — Musical  instruments  consist 
mostly  of  vibrating  strings  or  wires  whose  sound  is 
reinforced  by  the  forced  vibrations  of  sounding  boards, 
and  of  wind  instruments  in  which  a  partially  enclosed 
column  of  air  is  set  vibrating  by  resonance.  In  wind 
instruments  various  devices  are  used  for  setting  up  the 
vibrations  which  induce  the  resonance.  In  some  in- 
struments we  have  seen  this  is  accomplished  by  blowing 
across  a  sharp  edge,  in  some  a  small  reed  is  fixed  in 
the  mouthpiece  of  the  instrument  where  it  vibrates  to 
the  passage  of  the  air  as  do  the  reeds  of  a  mouth  organ 
or  an  accordeon,  and  in  some  the  lips  of  the  player 
serve  as  the  vibrating  instruments  to  which  the  air 
column  resounds. 

In  the  stringed  instruments  the  pitch  is  determined 
by  the  length,  weight,  and  tension  of  the  string,  and 
in  instruments  like  the  violin  and  guitar  the  pitch  of 
the  string  is  varied  while  playing  by  changing  its 
effective  length,  or  by  touching  it  so  that  it  will  vibrate 
in  segments  and  give  harmonics  of  its  fundamental 
tone.  In  wind  instruments  the  effective  length  of  the 
air  column  is  changed  by  various  devices,  such  as 
opening  or  closing  holes  in  the  sides  of  the  instrument 
or  by  opening  keys  into  auxiliary  tubes  whose  length 
is  thus  added  to  that  of  the  original  column. 

PROBLEMS  ON  SOUND. — When  the  velocity  of  sound  is  uoo 
feet  per  second,  a  glass  tube  5  feet  long  and  open  at  both 
ends  resounds  to  a  given  tuning  fork.  What  is  the  rate  of 
the  fork  ? 

A  brass  rod  i  meter  long  clamped  at  its  middle  and  pro- 
vided with  a  paper  disc  on  one  end  induces  wave  segments 
10  cm.  long  in  the  dust  particles  of  a  Kundt's  tube.  If  the 
velocity  of  sound  in  air  be  taken  as  338  meters  a  second, 
what  is  its  velocity  in  brass  ? 


236  PHYSICS 

The  velocity  of  sound  in  brass  is  .  7  its  velocity  in  glass. 
The  density  of  the  glass  is  2.5  and  that  of  the  brass  is  8.5; 
what  are  their  relative  elasticities  ? 

An  experiment  on  the  velocity  of  sound  in  carbon  dioxide 
gas  at  atmospheric  pressure  gave  260  meters  a  second  when 
the  velocity  in  air  was  332  meters.  What  is  the  specific 
gravity  of  carbon  dioxide  in  terms  of  air  ? 


PART   V 
MAGNETISM  AND  ELECTRICITY 

MAGNETISM 

PROPERTIES   OF   MAGNETS 

Natural  and  Artificial  Magnets. 

LABORATORY  EXERCISE  77. — Lay  a  piece  of  Lodestone 
(magnetic  iron  ore)  in  a  box  containing  tacks  or  iron  filings. 
What  peculiar  property  do  you  observe  in  the  lodestone  ? 
Do  all  parts  of  the  lodestone  seem  to  possess  this  property 
to  an  equal  degree  ? 

Try  the  same  experiment  with  a  small  bar  magnet.  With 
ysmall  horseshoe  magnet.  In  what  parts  of  these  artificial 
inl^nets  does  the  magnetic  property  seem  to  reside  ? 

Try  the  experiment  using  small  bits  of  other  substances  as 
well  as  iron  and  steel.  What  substances  may  be  attracted 
by  a  magnet  ? 

The  piece  of  lodestone  used  in  the  experiment  is  a  natural 
magnet.  It  is  a  piece  of  iron  ore  of  a  kind  which  is  found 
in  considerable  quantities  in  various  parts  of  the  world,  and 
is  often  called  Magnetite.  Its  chemical  formula  is  Fe3O4. 
It  was  formerly  found  in  large  quantities  about  Magnesia, 
an  ancient  city  near  Smyrna  in  Turkey,  and  is  supposed  by 
some  to  have  received  its  name  from  the  name  of  the  city. 

The  bar  magnet  and  the  horseshoe  magnet  are  made  of 
steel  and  are  accordingly  artificial  magnets.  The  regions 
about  which  the  magnetic  atractions  are  strongest  are  called 
Poles.  How  many  poles  has  each  of  the  artificial  magnets 
used  by  you  ? 

237 


238 


PHYSICS 


Magnetic  Poles. 

LABORATORY  EXERCISE  78. — Lay  a  knitting-needle  on  the 
table  and  stroke  it  several  times  always  in  the  same  direction 
and  with  the  same  pole  of  the  horseshoe  or  bar  magnet. 
Determine  if  the  knitting-needle  is  made  a  magnet  by  this 
process. 


FIG.  67. 

Cut  out  a  little  triangle  of  paper,  thrust  the  knitting- 
needle  through  it  as  shown  in  the  figure,  and  suspend  it  from 
one  corner  by  a  thread  without  torsion  so  that  the  needle 
will  be  supported  in  a  horizontal  position.  After  the  needle 
has  come  to  rest,  in  what  direction  does  it  lie  ?  See  that  it 
is  not  constrained  by  any  twist  in  the  thread. 

If  the  needle  always  comes  to  rest  in  the  same  position, 
mark  the  poles  so  that  you  can  tell  in  what  direction  they 
pointed,  and  prepare  another  knitting-needle  magnet  and 
test  it  in  the  same  way.  Call  one  pole  of  your  magnet  its 
North-seeking  pole  and  the  other  its  South-seeking  pole. 

Does  your  bar  magnet  have  North-seeking  and  South- 
seeking  poles  ? 


MAGNETISM  AND  ELECTRICITY  239 

Magnetic  Attractions  and  Repulsions. 

LABORATORY  EXERCISE  79. — Suspend  one  knitting-needle 
magnet  and  holding  the  other  in  the  hand  determine  whether 
there  is  an  attraction  or  a  repulsion  between  the  like  and  the 
unlike  poles  of  two  magnets.  State  the  law  of  magnetic 
attraction  and  repulsion  as  follows : 


Like  poles /  unlike  poles.. 


Without  suspending  the  horseshoe  magnet  determine 
which  is  its  north-seeking  and  which  its  south-seeking  pole. 

MAGNETIC   PERMEABILITY 

Magnetic  Permeability  of  Iron. 

LABORATORY  EXERCISE  80. — Lay  a  tack  on  a  piece  of  glass, 
place  a  magnet  on  the  other  side  of  the  glass  and  determine 
if  the  magnetic  attraction  acts  through  the  glass.  Repeat 
with  wood,  paper,  and  other  substances.  Substances 
through  which  the  magnetic  attraction  acts  are  said  to  have 
magnetic  permeability.  Do  you  find  any  substance  not 
permeable  to  magnetic  attraction  ? 

Hold  one  pole  of  a  bar  magnet  against  the  end  of  an  iron 
bar  a  foot  or  more  in  length  and  determine  if  the  magnetic 
attraction  acts  through  the  length  of  the  iron.  Which  is 
more  permeable  to  magnetic  attraction,  iron  or  wood  ? 

A  magnet  sealed  up  in  a  vacuum  can  still  attract  bodies 
outside,  hence  the  magnetic  attraction  does  not  depend  upon 
the  existence  of  intervening  matter.  Since  the  magnet  may 
exert  an  attracting  or  repelling  pressure  upon  another  mag- 
net across  a  vacuum,  this  pressure  must  be  transmitted  in 
some  medium  different  from  ordinary  matter.  This  medium 
is  supposed  to  be  the  same  medium  which  transmits  radiation 
and  is  called  the  Luminiferous  Ether.  The  reasons  for  this 
supposition  will  appear  later. 

The  magnetic  permeability  of  the  vacuum,  that  is,  of  the 
Ether,  is  nearly  the  same  as  in  most  bodies,  hence  it  is  sup- 
posed that  the  magnetic  pressure  through  these  bodies  is 
transmitted  by  the  Ether.  Since  the  permeability  of  iron  is 
so  much  greater  than  of  other  substances,  it  is  supposed  that 
the  Ether  is  in  some  way  greatly  modified  in  iron. 


240  PHYSICS 


THE   MAGNETIC   FIELD 

Definition. — The  entire  region  about  a  magnet  in 
which  the  magnetic  pressure  can  be  shown  to  exist  is 
called  the  Magnetic  Field.  Since  the  magnetic  pres- 
sure falls  off  gradually  from  the  vicinity  of  a  magnet 
and  becomes  zero  only  at  an  infinite  distance,  the 
magnetic  field  has  no  definite  boundaries.  In  practice, 
the  magnetic  pressure  cannot  be  detected  at  very  great 
distances  from  even  very  powerful  magnets. 

Magnetic  Induction. 

LABORATORY  EXERCISE  81. — Place  a  soft-iron  bar  several 
inches  long  with  one  end  very  near  but  not  in  contact  with 
one  pole  of  a  strong  magnet.  Determine  by  means  of  iron 
filings  or  small  tacks  if  the  iron  bar  has  magnetic  poles. 
Using  a  suspended  magnetic  needle,  determine  the  names  of 
these  poles.  Is  the  pole  nearest  to  the  magnet  like  or 
unlike  the  pole  of  the  magnet  nearest  to  it  ? 

Turn  the  magnet  so  that  its  other  pole  will  be  near  the 
end  of  the  bar.  Does  this  change  the  polarity  of  the  bar  ? 

Remove  the  magnet.  Does  the  bar  still  have  magnetic 
poles  ?  If  so,  are  they  as  strong  as  before  ? 

A  piece  of  iron  placed  in  the  magnetic  field  becomes  itself 
a  magnet.  In  this  case  the  iron  is  said  to  be  magnetized  by 
induction.  Thus  when  the  north-seeking  pole  of  a  magnet 
is  brought  near  one  end  of  an  iron  bar,  it  is  customary  to 
say  that  a  south-seeking  pole  is  induced  in  the  end  of  the 
bar  nearest  the  magnet  and  a  north-seeking  pole  in  the 
farther  end.  In  the  case  of  magnetic  induction,  does  the 
induced  pole  nearest  the  magnet  tend  to  attract,  or  repel, 
the  neighboring  magnetic  pole  ? 

Do  you  know  of  any  case  of  magnetic  attraction  which  is 
not  an  attraction  between  magnets  ? 

Magnetic  Force  within  a  Magnet. 

LABORATORY  EXERCISE  82. — We  have  seen  that  when  a 
piece  of  iron  is  placed  in  a  magnetic  field  the  magnetic  force 
acts  through  it  to  a  greater  distance  than  through  air,  and 
that  in  so  doing  it  makes  a  magnet  of  the  iron.  The  ques- 


MAGNETISM  AND  ELECTRICITY  241 

tion  properly  arises  whether  the  magnetic  force  acts  in  the 
same  way  through  a  permanent  magnet. 

File  a  magnetized  knitting-needle  or  piece  of  steel  spring 
nearly  in  two  and  break  it  off.  Are  there  magnetic  poles  at 
the  place  of  separation  ? 

Break  one  of  the  pieces  again.  Do  you  cause  two  more 
poles  to  appear  ?  Is  there  a  magnetic  force  acting  length- 
wise through  the  magnet  ?  Can  you  separate  a  north-seeking 
pole  and  a  south-seeking  pole  so  that  they  will  be  on  differ- 
ent pieces  of  magnet  ? 

This  experiment  shows  that  while  the  magnetic  pressure 
exists  within  the  magnet,  magnetic  poles  appear  only  where 
the  magnetic  force  can  be  said  to  pass  from  the  magnet  into 
the  air.  Accordingly  a  row  of  magnets  can  be  put  together 
with  their  unlike  poles  in  contact  and  form  but  one  magnet. 

All  attempts  to  break  a  magnet  into  small  enough  pieces 
to  separate  the  poles  have  failed.  Hence  it  is  supposed  that 
the  magnetic  polarity  extends  to  the  molecular  structure  of 
the  magnet. 

THE   MAGNETIC   CIRCUIT 


Relation  of  Magnetic  Poles  to  Permeability  of 
Medium  in  Magnetic  Field.  —  We  have  seen  that  the 
magnetic  field  outside  a  magnet  is  continuous  with  a 
magnetic  field  within  the  magnet.  Magnetic  poles 
seem  to  exist  where  the  magnetic  field  passes  from  one 
medium  to  another  of  different  permeability.  Thus  a 
piece  of  iron  placed  in  a  magnetic  field  has  magnetic 
poles  where  the  magnetic  field  enters  it  and  leaves  it. 
In  a  bar  or  horseshoe  magnet  the  magnetic  field  seems 
to  be  very  weak  outside  the  magnet  except  near  its 
ends. 

Lines  of  Magnetic  Force. 

LABORATORY  EXERCISE  83.  —  Place  the  piece  of  soft  iron, 
called  the  "  armature"  or  "  keeper,"  across  the  ends  of  a 
horseshoe  magnet.  What  effect  does  this  have  upon  the 
strength  of  the  magnetic  field  outside  the  magnet  ?  Does  a 
magnet  arranged  in  this  way  have  poles  strong  enough  to 
pick  up  tacks  ? 


242  PHYSICS 

Remove  the  soft  iron  and  test  the  strength  of  the  poles. 
What  do  you  conclude  in  regard  to  the  poles  of  a  magnet 
making  a  complete  ring  ? 

Before  placing  the  iron  across  the  poles  of  the  magnet,  the 
magnetic  field  in  the  air  was  very  strong  near  the  ends  of  the 
magnet.  With  the  iron  across  the  poles  the  field  seemed  to 
be  confined  principally  to  the  magnet  itself  and  to  the  piece 
of  iron.  It  is  customary  to  speak  of  a  magnetic  field  in 
which  no  poles  are  produced  as  forming  a  closed  circuit 
within  the  magnet  and  the  iron.  Thus  when  the  two  poles 
of  a  magnet  are  joined  by  a  substance  of  high  magnetic 
permeability  the  magnetic  pressure  seems  to  pass  through 
this  substance  from  one  magnetic  pole  to  the  other.  There 
is  no  reason  for  assuming  that  this  pressure  acts  in  one 
direction  more  than  in  another,  but  it  is  customary  to  speak 
of  the  direction  in  which  a  north-seeking  magnetic  pole 
would  be  impelled  as  the  positive  direction  of  the  magnetic 
force.  A  line  drawn  continuously  in  the  direction  in  which 
a  north-seeking  magnetic  pole  is  impelled  is  called  a  line  of 
magnetic  force,  since  such  a  line  shows  at  every  point  in  its 
course  the  direction  of  the  magnetic  force. 

Since  a  north-seeking  magnetic  pole  when  placed  in  a 
magnetic  field  is  repelled  by  another  north-seeking  pole,  and 
is  attracted  by  a  south-seeking  pole,  it  will  move  away  from 
the  north-seeking  pole  of  the  magnet  and  toward  its  south- 
seeking  pole.  A  line  of  magnetic  force  would  accordingly 
be  drawn  everywhere  away  from  the  north-seeking  pole  of 
the  magnet  and  toward  its  south-seeking  pole. 

To  Show  the  Direction  of  the  Lines  of  Magnetic 
Force. 

LABORATORY  EXERCISE  84. — Magnetize  a  sewing-needle  or 
a  piece  of  knitting-needle  about  four  or  five  centimeters  long. 
Thrust  its  north-seeking  end  in  a  small  cork  so  that  the 
needle  may  float  vertically  in  water  with  its  north-seeking 
pole  upward.  Rest  a  strong  bar  magnet  about  six  inches 
long  horizontally  upon  two  supports  just  above  the  surface 
of  water  in  a  vessel,  and  place  the  floating  needle  in  the 
water  at  a  short  distance  to  one  side  of  the  magnet.  Note 
the  direction  in  which  the  needle  is  impelled. 

Here  the  south-seeking  pole  of  the  needle  is  so  much 
farther  from  the  magnet  than  its  north-seeking  pole  that  the 


MAGNETISM  AND  ELECTRICITY  243 

magnetic  force  acts  principally  upon  the  north-seeking  pole 
of  the  needle. 

Draw  lines  indicating  the  direction  of  the  lines  of  magnetic 
force  in  the  field  near  a  magnet  and  farther  from  the  magnet. 
(Why  should  this  experiment  be  performed  in  a  vessel  free 
from  iron  ?) 

Judging  from  the  velocity  of  the  moving  needle  in  different 
parts  of  the  field,  is  the  magnetic  force  stronger  near  the 
magnet,  or  at  a  distance  from  it  ? 

We  have  already  seen  that  we  may  regard  the  poles  of  a 
magnet  as  the  place  where  the  magnetic  force  enters  or  leaves 
the  magnet.  Considering  the  positive  direction  of  the  lines 
of  magnetic  force,  what  kind  of  a  pole  is  produced  where 
the  lines  of  magnetic  force  enter  a  piece  of  iron  ? 

To  Trace  the  Lines  of  Force  by  Means  of  a  Mag- 
netic Needle. 

LABORATORY  EXERCISE  85. — Lay  a  bar  magnet  upon  the 
table  and  by  means  of  a  small  compass  or  other  mounted 
magnetic  needle  determine  if  one  magnet  brought  into  the 
field  of  another  magnet  tends  to  set  itself  so  that  the  lines  of 
magnetic  force  enter  at  one  pole  and  leave  at  the  other.  If 
so,  at  which  pole  do  they  enter  ?  Show  how  to  draw  the 
direction  of  the  lines  of  magnetic  force  by  means  of  the 
mounted  magnetic  needle. 

Mapping  the  Lines  of  Magnetic  Force  by  Means  of 
Iron  Filings. 

LABORATORY  EXERCISE  86. — We  have  seen  that  a  piece  of 
iron  in  a  magnetic  field  becomes  a  magnet  with  a  south- 
seeking  pole  where  the  lines  of  magnetic  force  enter  it  and  a 
north-seeking  pole  where  the  lines  of  magnetic  force  leave 
it.  .  If  a  large  number  of  small  pieces  of  iron  are  placed  near 
together  in  a  magnetic  field  they  will  accordingly  become 
magnets  and  cling  together,  the  north-seeking  pole  of  one 
attracting  the  south-seeking  pole  of  another. 

Lay  a  horseshoe  magnet  upon  the  table  and  lay  a  piece  of 
stiff  paper  upon  it.  Sprinkle  iron  filings  slowly  upon  the 
paper  from  a  height  of  about  ten  centimeters,  and  tap  the 
paper  gently  until  they  have  taken  some  definite  arrange- 
ment. 


244  PHYSICS 

What  reason  have  you  for  believing  that  the  iron  filings 
are  magnetized  ? 

Can  you  regard  a  single  row  of  the  iron  filings  as  a  long, 
flexible  magnet  ?  Why  ?  Does  such  a  row  of  iron  filings 
lie  in  the  direction  of  a  line  of  magnetic  force  ? 

Sketch  the  lines  of  magnetic  force  about  the  poles  of  a 
horseshoe  magnet. 

Using  iron  filings  in  the  same  manner,  sketch  the  Jines  of 
magnetic  force  about  the  poles  of  a  horseshoe  magnet  with 
a  piece  of  iron  lying  near  but  not  in  contact  with  the  poles. 

By  means  of  iron  filings,  make  sketch  maps  of  the  lines  of 
magnetic  force  about  a  single  bar  magnet,  about  two  bar 
magnets  lying  side  by  side  with  their  like  poles  in  the  same 
direction  and  with  their  like  poles  in  opposite  directions. 

Do  the  lines  of  magnetic  force  ever  run  from  one  pole  to 
another  pole  of  the  same  name  ? 

When  do  the  lines  of  magnetic  force  of  one  magnet  pass 
readily  through  another  magnet  ? 

Theory  of  Magnetic  Curves. — Careful  experiments 
have  shown  that  the  attraction  or  repulsion  between 
two  magnetic  poles  decreases  as  the  square  of  the  dis- 
tance between  them  increases.  Thus  if  the  attraction 
or  repulsion  between  two  magnetic  poles  at  a  distance 
of  one  centimeter  be  n  dynes,  at  a  distance  of  two 

centimeters   it  will  be  —  dynes,  and  at  a  distance  of 

4 

three  centimeters  it  will  be  -  dynes. 

Make  a  diagram  as  in  Fig.  68,  showing  the  position  of  the 
poles  of  a  bar  magnet,  and  locate  a  point  P  twice  as  far  from 
the  south-seeking  as  from  the  north-seeking  pole  of  the 
magnet.  Let  the  point  P  represent  a  north-seeking  mag- 
netic pole,  and  assume  both  poles  of  the  magnet  to  be 
equally  strong.  P  will  then  be  repelled  by  the  north-seeking 
pole  of  the  magnet  four  times  as  much  as  it  will  be  attracted 
by  the  south-seeking  pole.  Draw  lines  representing  the 
direction  and  magnitude  of  the  two  forces  acting  upon  P, 
and  determine  the  direction  of  their  resultant. 


MAGNETISM  AND  ELECTRICITY  245 

Make  the  same  determination  when  P  is  two  thirds  as  far 
from  the  north-seeking  as  from  the  south-seeking  pole. 


N 


FIG.  68. 


How  does  the  direction  of  the  magnetic  force  as  deter- 
mined above  seem  to  agree  with  the  direction  as  determined 
by  the  other  methods  ? 

THE    EARTH   A   MAGNET 

The  Earth's  Magnetic  Field.  —  We  have  seen  that 
the  suspended  magnetic  needle  tends  to  lie  in  a  direc- 
tion nearly  north  and  south.  If  there  are  horizontal 
lines  of  magnetic  force  about  the  earth,  in  what  direc- 
tion do  they  run  ? 

The  Dipping  Needle. 

LABORATORY  EXERCISE  87.  —  Balance  an  unmagnetized 
knitting-needle  on  a  horizontal  axis  by  thrusting  it  through 
a  piece  of  cork  through  which  another  needle  is  thrust  at 
right  angles  to  it  to  serve  as  an  axis.  After  the  needle  is 
carefully  balanced  magnetize  it  without  changing  its  position 
in  the  cork,  and  place  it  parallel  to  the  suspended  horizontal 
needle.  Are  the  lines  of  magnetic  force  about  the  earth 
horizontal  ?  If  not,  in  what  direction  do  they  dip  ? 

The  horizontal  and  the  dipping  needle  indicate  that  the 
earth  has  a  magnetic  field.  If  this  is  true,  a  piece  of  iron 


246  PHYSICS 

placed  in  the  proper  position  in   the  earth's  field   should 
become  a  magnet. 

Magnetic  Induction  of  the  Earth. 

LABORATORY  EXERCISE  88. — Set  the  dipping  needle  so  that 
it  points  to  the  magnetic  north  (The  magnetic  north  may 
not  be  the  true  north),  and  note  the  direction  of  the  earth's 
lines  of  magnetic  force.  Hold  a  bar  of  very  soft  iron  a  foot 
or  more  in  length  at  some  distance  from  the  magnetic  needle 
and  parallel  to  the  earth's  lines  of  magnetic  force.  Will  its 
end  now  attract  iron  filings  ?  Will  it  repel  either  end  of  a 
compass  needle  if  brought  slowly  near  it  ? 

Holding  it  still  in  this  direction,  strike  it  several  sharp 
blows  on  the  end  with  a  hammer.  Is  its  magnetic  strength 
increased  or  diminished  by  this  treatment  ? 

Turn  the  bar  east  and  west.  Is  it  still  a  magnet  ?  If  so, 
strike  the  end  as  before.  How  does  this  affect  its  mag- 
netization ? 

See  if  you  can  reverse  the  magnetization  of  the  bar  by 
changing  it  end  for  end  in  the  magnetic  field  without  strik- 
ing it  with  the  hammer.  Look  for  a  very  small  repulsion 
of  the  needle. 

Write  out  your  reasons  for  believing  the  earth  to  be  a 
magnet. 

Magnetic  Curves  of  the  Earth. — In  latitude  about 
70°  N.  and  longitude  nearly  97°  W.  the  dipping  needle 
stands  vertical.  This  is  called  the  north  magnetic  pole 
of  the  earth.  Do  the  lines  of  magnetic  force  enter,  or 
leave  the  earth  at  this  point  ?  Is  it  a  north-seeking, 
or  a  south-seeking  magnetic  pole  ?  Do  you  see  any 
objection  to  calling  the  north-seeking  pole  of  a  magnet 
its  north  pole  ? 

The  south  magnetic  pole  of  the  earth  lias  recently 
been  located  in  73°  20'  S.  latitude  and  148°  E.  longi- 
tude. From  what  we  have  learned  of  the  magnetic 
curves  of  a  steel  magnet,  we  should  expect  a  magnetic 
needle  anywhere  on  the  earth  to  lie  with  its  ends 
pointing  toward  these  two  magnetic  poles,  This  is 


MAGNETISM  AND  ELECTRICITY  247 

not  always  the  case.      In  many  parts  of  the  earth  the 
needle  varies  considerably  from  this  direction. 


MAGNETIC    STRENGTH    OF    FIELD 

Definitions. — A  unit  magnetic  pole  is  defined  as  one 
which  will  repel  a  similar  and  equal  pole  placed  at  a 
distance  of  one  centimeter  from  it  in  air  with  a  force  of 
one  dyne.  A  magnetic  field  in  which  a  unit  pole 
would  be  acted  upon  by  a  pressure  of  one  dyne  is  called 
a  field  of  unit  strength. 

It  is  common  in  works  on  magnetism  to  express  the 
strength  of  a  magnetic  field  in  terms  of  lines  of  mag- 
netic force.  Hitherto  we  have  used  the  term  "  line  of 
magnetic  force  ' '  to  indicate  only  the  direction  of  the 
pressure  upon  a  magnetic  pole  in  a  magnetic  field.  It 
is  customary  to  also  give  a  quantitative  value  to  the 
line  of  magnetic  force,  and  to  say  that  a  magnetic  field 
of  unit  strength  is  one  which  has  one  line  of  magnetic 
force  to  the  square  centimeter. 

A  field  which  exerts  a  pressure  of  10  dynes  on  a  unit 
magnetic  pole  is  said  to  have  a  field  strength  of  10  lines 
to  the  square  centimeter,  and  the  like.  This  is  an 
unfortunate  method  of  expressing  the  intensity  of  mag- 
netic action,  since  there  is  no  reason  for  believing  that 
certain  parts  of  the  Ether  in  the  magnetic  field  differ  in 
their  properties  from  other  parts. 

The  high  magnetic  permeability  of  iron  is  expressed 
in  terms  of  lines  of  force  by  saying  that  iron  is  a  better 
carrier  of  lines  of  force  than  air.  Thus  the  magnetic 
field  induced  through  iron  by  a  magnet  is  many  times 
as  strong  as  the  field  induced  through  air  at  the  same 
distance  from  the  magnet,  Iron  is  accordingly  said  to 


248  PHYSICS 

permit  the  passage  of  many  more  lines  of  force  than  air 
for  the  same  magnetic  pressure. 
Questions  on  Magnetism. 

A  compass  is  placed  at  some  distance  from  one  of  the  poles 
of  a  bar  magnet.  Will  the  action  of  the  magnet  upon  the 
compass  needle  be  increased  or  diminished  by  placing  a 
piece  of  soft  iron  between  it  and  the  magnet  but  not  in  con- 
tact with  the  magnet  ?  Why  ? 

A  compass  is  placed  at  an  equal  distance  from  both  poles 
of  a  horseshoe  magnet;  will  the  directive  action  of  the 
magnet  be  increased  or  diminished  by  placing  a  single  piece 
of  iron  between  it  and  both  magnetic  poles  ?  Why  ? 

A  compass  is  placed  in  a  magnetic  field  and  is  surrounded 
by  a  cylinder  of  iron.  Is  the  influence  of  the  magnetic  field 
upon  the  compass  increased  or  diminished  by  the  iron  ? 
Explain  ? 

Will  the  works  of  a  watch  in  an  iron  case  be  more  or  less 
liable  to  become  magnetized  than  in  a  case  of  some  other 
metal  ? 

Will  a  magnetic  needle  floated  on  a  cork  in  water  tend  to 
move  toward  the  north  magnetic  pole  of  the  earth  ?  Why  ? 


ELECTROSTATICS 

ELECTRIFICATION 

Electrification  of  Sealing  Wax  and  Glass. 

LABORATORY  EXERCISE  89.  —  Suspend  a  light  body,  as  a 
pith  ball,  an  egg  shell,  or  a  paper  cylinder  by  a  thread  a  foot 
or  more  in  length.  Rub  a  clean,  dry  stick  of  sealing  wax 
gently  with  a  piece  of  warm,  dry,  woolen  cloth,  or  brush  it 
with  fur,  a  feather  duster,  or  a  clothes  brush  not  made  of 
vegetable  fiber.  Bring  the  rubbed  end  of  the  sealing  wax 
near  the  suspended  body  and  observe  if  a  force  is  exerted 
between  them.  If  so,  the  sealing  wax  is  Electrified. 

See  if  the  electrified  sealing  wax  can  be  made  to  attract 
other  light  bodies.  Balance  a  meter  stick  or  a  long  board 
on  the  round  top  of  a  glass  bottle  stopper  or  other  suitable 
support  and  see  if  you  can  cause  it  to  rotate  by  the  attrac- 
tion of  the  electrified  sealing  wax. 


MAGNETISM  AND  ELECTRICITY  249 

Instead  of  the  sealing  wax,  use  a  clean,  dry  glass  rod  or 
piece  of  glass  tubing  whipped  or  gently  rubbed  with  a  piece 
of  silk.*  Is  the  glass  electrified  ?  Can  you  electrify  it  as 
strongly  with  the  woolen  as  with  the  silk  ? 

Try  to  electrify  hard  rubber,  sulphur,  rubber  tubing, 
porcelain,  metal,  wood.  Which  ones  can  you  electrify  ? 
Does  it  make  a  difference  which  material  is  used  as  a  rubber  ? 

Origin  of  Name  Electrification. — The  phenomenon 
of  electric  attraction  was  known  to  the  Greeks  at  least 
2500  years  ago.  It  was  first  discovered  in  rubbed 
amber,  and  was  explained  by  Thales,  B.C.  580,  by 
attributing  to  amber  a  kind  of  life.  The  Greek  word 
for  amber  is  Elektron,  and  this  condition  of  rubbed 
amber  came  to  be  called  Electrification.  The  amber 
or  sealing  wax  when  in  this  condition  is  said  to  be 
Electrified,  or  to  have  an  Electric  Charge. 

Electrics  and  Non-electrics. — This  was  practically 
all  that  was  known  of  electrification  for  more  than  2000 
years.  In  the  year  1600,  Dr.  William  Gilbert, 
physician  to  Queen  Elizabeth,  of  England,  published 
the  fact  that  many  other  bodies  besides  amber  are 
capable  of  electrification.  He  classified  bodies  as 
Electrics  and  Non-electrics,  according  as  he  found  them 
capable  or  incapable  of  being  electrified. 

Electric  Repulsion. 

LABORATORY  EXERCISE  90. — Electrify,  as  before,  one  end 
of  a  stick  of  sealing  wax,  and  taking  care  not  to  touch  the 
electrified  part,  suspend  it  horizontally  in  a  stirrup  made  of 
bent  tin  or  wire  and  supported  by  a  string  a  foot  or  more 
long.  A  piece  of  very  narrow  silk  ribbon  ("  baby  "  ribbon) 

*  All  the  materials  used  in  the  experiments  on  static  electricity  must 
be  kept  very  clean  and  dry.  In  moist  weather  they  must  be  warmer 
than  the  air  in  the  room  and  must  not  be  handled  on  the  parts  which  it  is 
wished  to  electrify.  They  may  be  cleared  from  grease  by  washing  with 
gasoline  on  a  clean  cloth. 


250 


PHYSICS 


makes  an  excellent  supporting  string,  as  it  has  no  torsion, 
and  will  be  found  useful  in  later  experiments. 

Hold  the  finger  near  the  electrified  end  of  the  sealing  wax. 
Does  the  finger  attract  the  sealing  wax  ?  Would  this  neces- 
sarily follow  from  what  you  know  about  force  ?  Robert 
Boyle  announced  this  as  a  discovery  in  1675.  Which  one 


FIG.  69. 

of  Newton's  Laws  of  Motion  was  not    comprehended  by 
Boyle  ? 

Electrify  another  stick  of  sealing  wax,  and  bring  its  elec- 
trified end  near  the  electrified-  end  of  the  suspended  sealing 
wax.  Make  sure  that  the  suspended  sealing  wax  has  not 
lost  its  electrification.  What  kind  of  a  force  is  exerted 
between  two  similarly  electrified  bodies  ? 

The  phenomenon  of  electric  repulsion  was  discovered  by 
Otto  von  Guericke,  of  Magdeburg.  What  important  inven- 
tion do  we  owe  to  von  Guericke  ? 

Will  a  glass  rod  electrified  by  silk  attract  or  repel  the 
electrified  sealing  wax  ? 

Suspend  a  glass  rod  electrified  by  silk  and  see  if  it  is 
repelled  by  another  glass  rod  similarly  electrified. 

Find  whether  a  piece  of  sulphur  electrified  by  woolen  is 
electrified  like  the  sealing  wax  or  like  the  glass. 


MAGNETISM  AND  ELECTRICITY  251 

What  is  the  character  of  the  electric  force  between  similarly 
electrified  bodies  ?  Between  dissimilarly  electrified  bodies  ? 
Where  have  you  seen  analogous  forces  ? 


x* 

-ified 


Two  Kinds  of  Electrification. — Bodies  electrifu 
like  glass  rubbed  with  silk  are  said  to  be  * '  Vitreously  ' ' 
electrified,  or  to  have  "Vitreous  electrification." 
Bodies  electrified  like  sealing  wax  rubbed  with  wool 
or  fur  are  said  to  have  "Resinous  electrification." 
Since  all  electrified  bodies  will  repel  either  the  electri- 
fied glass  or  the  electrified  sealing  wax,  we  know  of 
only  these  two  kinds  of  electrification.  (Why  may  we 
not  test  the  character  of  electrification  by  attractions 
instead  of  repulsions  ?) 

Transference  of  Electrification  by  Contact. 

LABORATORY  EXERCISE  91. — Suspend  a  light  pith  ball*  by 
a  dry  silk  thread  one  or  two  feet  in  length.  (The  thread 
should  not  be  drawn  through  the  hand  or  over  any  unclean 
surface.)  Bring  an  electrified  stick  of  sealing  wax  near 
enough  that  the  pith  ball  may  be  drawn  to  it  and  come  in 
contact  with  it.  Does  the  pith  ball  receive  electrification 
from  the  sealing  wax  ?  Does  the  sealing  wax  lose  all  or 
only  a  part  of  its  electrification  to  the  ball  ? 

Bring  a  similarly  suspended  pith  ball  near  the  first  one  and 
allow  them  to  be  drawn  together.  Is  the  electrification  now 
divided  between  them  ?  Do  the  pith  balls  have  vitreous  or 
resinous  electrification  ? 

Opposite  Character  of  Two  Kinds  of  Electrification. 

LABORATORY  EXERCISE  92. — Electrify  one  of  the  suspended 
pith  balls  from  glass  and  the  other  from  sealing  wax  and  then 
allow  them  to  come  in  contact  with  each  other.  Is  their 
electrification  strengthened  or  weakened  by  the  contact  ? 
What  is  the  character  of  the  charge,  if  any,  on  each  after 

*  Pith  balls  suitable  for  these  experiments  may  be  made  from  the 
dried  pith  of  various  vegetable  stems.  Sunflower  pith  is  especially 
adapted  to  this  purpose.  The  balls  should  be  cut  out  with  a  sharp 
knife,  and  should  be  smoothed  by  gently  rolling  them  between  the 
hands. 


252  PHYSICS 

contact  ?  Can  you  so  electrify  the  two  balls  that  after  con- 
tact neither  of  them  will  be  electrified  ?  Can  you  so  electrify 
them  that  after  contact  both  will  have  resinous  charges  ? 

Use  of  Terms  Positive  and  Negative. — We  have 
seen  reasons  for  the  belief  that  the  two  kinds  of  elec- 
trification represent  opposite  conditions  of  the  electrified 
body,  and  this  opposite  character  has  been  expressed 
by  the  terms  positive  and  negative.  Just  as  the  alge- 
braic addition  of  numerically  equal,  positive,  and  nega- 
tive quantities  produces  zero,  so  the  addition  of  so-called 
equal  quantities  of  vitreous  and  resinous  electrification 
produces  zero  electrification. 

There  is  no  known  reason  for  regarding  one  kind  of 
electrification  as  positive  rather  than  the  other ;  but  by 
general  agreement  the  vitreous  electrification  has  been 
called  positive  and  the  resinous  negative.  These  two 
kinds  of  electrification  are  accordingly  marked  with  the 
signs  +  and  --  just  as  are  the  algebraic  quantities. 

Simultaneous  Production  of  Both  Kinds  of  Electri- 
fication. 

LABORATORY  EXERCISE  93. — Suspend  the  two  pith  balls  at 
a  distance  of  a  foot  or  more  apart  and  electrify  them  oppo- 
sitely. Take  a  small  piece  of  flannel  attached  to  a  handle 
of  sealing  wax  by  sticking  it  to  the  wax  or  sewing  it  around 
the  end  of  the  stick,  and  holding  to  the  sealing-wax  handle, 
rub  another  stick  of  sealing  wax  with  the  flannel.  Is  the 
sealing  wax  electrified  as  usual  ?  Is  the  flannel  also  electri- 
fied ?  If  so,  what  is  the  character  of  its  electrification  ? 

With  a  piece  of  silk  attached  in  the  same  way  to  a  sealing- 
wax  handle,  electrify  a  glass  rod.  Is  the  silk  also  electrified  ? 
If  so,  what  is  the  character  of  its  electrification  ?  (Take  care 
that  the  sealing-wax  handles  to  which  the  silk  and  flannel 
are  attached  are  not  electrified.) 

Try  to  electrify  the  pieces  of  silk  and  flannel  by  rubbing 
them  together.  Give  results.  Are  both  kinds  of  electrifica- 
tion produced  at  the  same  time  ? 


MAGNETISM  AND  ELECTRICITY  253 

The  Electrostatic  Series.  —  The  four  substances 
which  you  have  used  to  produce  electrification  may  be 
arranged  in  a  series  such  that  when  any  two  are  rubbed 
together  the  one  higher  on  the  list  will  be  positively 
electrified  and  the  one  lower  on  the  list  negatively 
electrified.* 

This  series  is  called  the  Electrostatic  Series.  The 
following  substances  are  arranged  in  such  a  series: 
Fur,  Flannel,  Feathers,  Quartz,  Glass,  Cotton,  Linen, 
Silk,  Wood,  Metals,  Sulphur. 

What  would  be  the  character  of  the  electrification  produced 
on  quartz  by  rubbing  it  with  fur  ?  With  silk  ?  Do  your 
experiments  on  the  electrification  of  glass  justify  its  position 
between  flannel  and  silk  in  the  series  ? 

The  experiments  which  follow  are  best  performed 
by  means  of  an  electric  machine,  though  in  a  favorable 
climate  they  may  all  be  performed  without  one.  The 
principles  involved  in  the  construction  of  the  electric 
machine  are  not  discussed  here,  since  several  different 
kinds  of  electrical  machines  are  used.t  At  present  it 
will  be  regarded  as  an  instrument  for  producing  readily 
an  electrification  of  either  kind  desired.  For  this  pur- 
pose the  electric  machine  should  be  charged  and  the 
character  of  the  electrification  of  its  discharging  knobs 
should  be  tested  by  means  of  the  charged  pith  ball. 

ELECTRIC   CONDUCTION 

Conductors  and  Non-conductors. 

LABORATORY  EXERCISE  94. — Place  a  convenient  body  of 
wood  or  metal  on  a  glass  support  (a  potato  resting  on  a 

*  Owing  to  differences  in  glass,  the  relative  positions  of  glass  and 
flannel  are  sometimes  uncertain. 

f  The  teacher  should  explain  the  machine  he  uses  when  in  his 
opinion  his  class  is  prepared  for  it. 


254  PHYSICS 

glass  tumbler  or  beaker  is  as  good  as  anything),  and  attach 
to  it  a  pith  ball  or  cork  suspended  by  a  short  linen  thread 
so  that  it  will  hang  in  contact  with  the  body.  Lay  a  wire 
from  one  discharging  knob  of  the  electric  machine  to  the 
body,  and  try  whether  you  can  electrify  the  body  from  the 
machine.  Bodies  which  allow  electrification  to  pass  along 
them  are  called  conductors.  Test  and  classify  as  conductors 
and  non-conductors  glass,  sealing  wax,  rubber,  silk,  wood, 
metals,  threads  of  different  kinds,  etc. 

Why  were  your  pith  balls  in  former  experiments  suspended 
by  silk  threads  ?  Why  should  these  threads  be  dry  ?  Why 
is  the  body  used  in  these  experiments  mounted  upon  a  glass 
support  ?  Why  were  the  pieces  of  silk  and  flannel  mounted 
on  sealing  wax  ?  Why  did  Dr.  Gilbert  fail  to  electrify  his 
"  non-electric  "  substances  when  held  in  his  hand  ?  What 
new  classification  can  you  substitute  for  electrics  and  non- 
electrics  ? 

Insulators. — Non-conducting  bodies  are  also  called 
Insulators,  because  they  must  be  interposed  between 
electrified  conducting  bodies  and  the  earth  if  these 
bodies  are  to  retain  their  electrification.  No  body  is  a 
perfect  insulator,  but  some  bodies  allow  electrification 
to  escape  very  slowly.  In  the  experiments  which 
follow  where  perfect  insulation  is  desired  a  block  of 
hard  paraffin  or  sealing  wax  or  a  silk  thread  or  ribbon 
support  will  serve  the  best.  The  success  of  all  elec- 
trical experiments  depends  upon  careful  insulation  of 
all  charged  bodies.  Glass  is  frequently  a  very  poor 
insulator,  and  frequently  a  conducting  layer  of  moisture 
gathers  on  its  surface.  Its  insulating  properties  are 
often  improved  by  washing  with  gasoline.  The  suc- 
cessful working  of  an  electric  machine  depends  upon 
the  careful  insulating  of  the  different  parts,  and  many 
good  machines  are  discarded  when  they  need  only  a 
careful  cleaning  and  drying. 


MAGNETISM  AND  ELECTRICITY 


255 


ELECTROSTATIC    INDUCTION 

Electrification  by  Induction. 

LABORATORY  EXERCISE  95. — Suspend  two  pith-ball  pendu- 
lums or  other  light  conductors  by  silk  threads  about  10 
centimeters  long  and  about  10  centimeters  apart,  and  lay  a 
fine  wire  long  enough  to  reach  from  one  to  the  other  lightly 
upon  them.  Bring  an  electrified  stick  of  sealing  wax  or  a 


FIG.  70. 

conductor  electrified  by  the  machine  near  enough  to  one 
pendulum  to  attract  the  pendulum  and  cause  the  wire  to  fall 
off,  but  do  not  let  the  charged  body  touch  the  pendulum. 

Remove  the  electrified  body,  and  test  both  pendulums  for 
electrification.  Are  they  similarly  or  oppositely  electrified  ? 
How  does  the  electrification  on  the  one  nearest  the  charged 
body  compare  with  the  electrification  of  the  body  ?  To  what 
phenomenon  in  magnetism  is  electrostatic  induction  com- 
parable ? 

Bring  an  electrified  body  near  a  silk  suspended  pith  ball, 
and  while  holding  it  in  this  position  touch  the  pith  ball  with 
your  hand.  Remove  the  hand  and  then  the  charged  body. 
Is  the  pith  ball  electrified  ?  How  does  the  character  of  its 
electrification  compare  with  that  of  the  inducing  charge? 
What  was  the  purpose  of  touching  the  ball  with  the  hand  ? 
How  can  you  electrify  several  bodies  from  a  single  electrified 


256  PHYSICS 

body  without  decreasing  the  original  charge  ?     Will  they  be 
electrified  like  or  unlike  the  original  charge  ? 

Equality  of  Induced  +  and  —  Charges. — You  have 
seen  that  an  electrified  body  brought  near  an  insulated 
conductor  induces  both  positive  and  negative  electrifica- 
tion upon  the  conductor.  If  the  charged  body  be 
removed  before  either  kind  of  electrification  is  allowed 
to  escape  from  the  conductor,  it  will  show  no  charge ; 
hence  the  two  kinds  of  electrification  must  be  induced 
in  quantities  just  sufficient  to  neutralize  each  other. 
We  accordingly  call  these  quantities  equal  in  magni- 
ude. 

Maxwell  says:*  "  No  force,  either  of  attraction  or 
repulsion,  can  be  observed  between  an  electrified  body 
and  a  body  not  electrified. ' '  How  can  you  harmonize 
this  statement  with  the  observations  upon  electric 
attraction  and  repulsion  which  you  have  made  ? 

The  Elect rophorus. — A  cake  of  some  non-conduct- 
ing substance,    as   sealing  wax   or    paraffin,    may  be 
^^  ele'ctrified   by  brushing  it  with 

JB  wool  or  fur,  and  may  then  be 

used  to  electrify  by  means  of 
induction  an  insulated  metal 
plate.  This  instrument  is  called 
an  Electrophorus.  Thus  a  cake 
/ \  of  hard  paraffin  is  melted  and 

/          \  allowed  to  cool  on  a  tin  plate. 

[  .».  4.  +  '+.  .4. .+.  +.  +.  +^-|      It   is    then    electrified,    and    a 
**j  metal  disc  or  smaller  tin  plate 
with    an     insulating    handle    is 
IG*  7I'  placed  flat  upon  it.     On  account 

of  the  uneven   surface  of  the  paraffin  the   metal  will 

*  Electricity  and  Magnetism,  Vol.  I,  p.  33. 


MAGNETISM  AND  ELECTRICITY  257 

touch  it  at  only  a  few  points,  and  will  not  carry  off 
much  of  its  electrification.  Fig.  71  indicates  the  dis- 
tribution of  the  electrification  on  the  metal  plate  at  this 
stage  of  the  experiment.  If  now  the  metal  be  touched 
by  the  hand  and  then  raised  by  its  insulating  handle  it 
will  be  found  highly  electrified,  and  may  be  used  instead 
of  an  electric  machine  for  charging  other  bodies.  It 
may  be  charged  in  this  way  many  times  without  per- 
ceptibly weakening  the  charge  on  the  paraffin. 

The  Bound  Charge. — You  have  seen  that  it  is  im- 
possible to  remove  the  negative  electrification  induced 
by  a  positive  charge,  or  vice  versa,  by  touching  it  with 
the  hand  while  the  inducing  charge  remains  near  it. 
When  the  inducing  charge  is  withdrawn  the  induced 
electrification  is  readily  removed.  The  induced  charge 
is  accordingly  said  to  be  bound  by  the  inducing  charge. 
Since  there  are  always  conductors  in  the  vicinity  of 
a  charged  body,  there  are  always  bound  charges  upon 
these  conductors.  Every  electrified  body  is  accordingly 
surrounded  by  oppositely  electrified  bodies. 

THE   ELECTRIC   FIELD 

Electric  Attraction  and  Repulsion  Due  to  the 
Medium  Surrounding  the  Charge.— We  have  seen  that 
an  electrified  body  is  capable  of  exerting  a  pressure 
upon  another  electrified  body  brought  near  it.  The 
region  in  which  this  pressure  can  be  observed  is  called 
the  Electric  Field. 

Since  any  electrified  body  induces  a  bound  charge 
upon  conductors  surrounding  it,  the  electric  field  is 
always  bounded  by  positive  and  negative  charges. 
Within  this  field  a  positively  electrified  body  is  always 
impelled  from  the  positive  to  the  negative  charge,  and 


258  PHYSICS 

a  negatively  electrified  body  from  the  negative  to  the 
positive  charge.  This  tendency  to  movement  is  due 
to  some  kind  of  a  pressure  exerted  upon  the  electrified 
body  by  the  medium  of  which  the  electric  field  is  com- 
posed. 

The  Dielectric  and  Electric  Elasticity.  —  The 
medium  which  constitutes  the  electric  field  and  which 
is  bounded  by  the  two  opposite  electrifications  is  called 
the  Dielectric.  Since  the  electric  pressure  resembles 
the  pressure  exerted  by  elastic  substances,  Maxwell 
has  called  the  property  of  the  dielectric  by  means  of 
which  it  exerts  a  pressure  upon  electrified  bodies  its 
Electric  Elasticity. 

The  Luminiferous  Ether  a  Dielectric. — Since  the 
electric  pressure  is  exerted  in  a  vacuum  as  well  as  in 
air,  the  vacuum  must  have  electric  elasticity.  The 
only  known  medium  existing  in  the  vacuum  is  the 
Luminiferous  Ether,  and  we  shall  later  see  the  best  of 
reasons  for  believing  that  the  electric  pressure  is  due 
to  the  Luminiferous  Ether,  and  that  the  Ether  may 
become  a  dielectric. 

Lines  of  Electric  Force. — The  electric  field  is  accord- 
ingly a  condition  set  up  in  the  dielectric.  This  condi- 
tion is  such  that  a  positively  electrified  body  is  impelled 
in  one  direction  and  a  negatively  electrified  body  in  the 
opposite  direction.  The  electric  field,  like  the  magnetic 
field,  may  accordingly  be  said  to  have  lines  of  force. 
The  direction  in  which  a  positively  electrified  body  is 
impelled  is  called  the  positive  direction  of  the  lines  of 
electric  force.  Where  the  lines  of  electric  force  leave 
a  conductor  we  have  the  condition  known  as  positive 
electrification.  Where  they  enter  a  conductor,  we  have 
negative  electrification.  An  insulated  conductor  placed 


MAGNETISM  AND  ELECTRICITY  259 

in  the  electric  field  has  positive  electrification  on  one 
side  and  negative  electrification  on  the  other,  just  as  a 
piece  of  iron  placed  in  the  magnetic  field  has  a  north- 
seeking  pole  on  one  side  and  a  south-seeking  pole  on 
the  other.  When  a  conductor  in  the  electric  field  is 
in  electric  communication  with  the  earth  its  lines  of 
electric  force  on  one  side  run  along  the  conductor  to 
or  from  the  earth  and  only  the  electrification  of  the 
bound  charge  appears  upon  the  conductor.  Thus  if 
the  earth  were  made  of  iron,  or  if  its  magnetic  perme- 
ability were  as  great  as  that  of  iron,  a  piece  of  iron  in 
a  magnetic  field  and  in  contact  with  the  earth  would 
show  only  one  magnetic  pole. 

To  Show  the  Effect  of  Surrounding  Conductors 
upon  the  Electric  Field. 

LABORATORY  EXERCISE  96. — A  thin  metal  plate,  as  a  piece 
of  tin  or  sheet  copper,  has  its  edges  and  corners  carefully 
rounded  off  with  a  file  and  is  supported  vertically  by  some 
insulating  material.  It  may  be  suspended  by  two  silk 
ribbons,  or  mounted  on  hard  rubber,  sealing  wax,  or  paraffin. 
Attach  two  similar  pith  or  cork  balls  to  opposite  sides  of  the 
plate  by  short  linen  threads  so  that  they  will  hang  against 
the  plate.  Remove  all  other  conductors  to  some  distance 
from  the  plate  and  electrify  it  until  the  pendulums  stand  out 
to  some  distance  from  the  plate.  Note  that  they  are  repelled 
equally  on  both  sides.  This  indicates  that  the  electric  field 
is  the  same  on  both  sides  of  the  plate. 

Bring  a  similarly  insulated  unelectrified  plate  with  pith- 
ball  pendulums  near  on  one  side  and  notice  that  the  electric 
field  passes  through  the  second  plate  without  greatly  affect- 
ing the  distribution  of  the  field  about  the  first  plate.  Bring 
the  second  plate  in  communication  with  the  earth  by  touch- 
ing it  with  the  finger.  Does  the  electric  field  now  pass 
through  it  ?  What  change  has  occurred  in  the  distribution 
of  the  field  about  the  electrified  plate  ? 

Holding  the  finger  against  the  sacond  plate,  bring  it  nearer 
to  the  electrified  plate.  The  pith  balls  now  take  the  posi- 


260 


PHYSICS 


tions  shown  in  Fig.  72.  Is  the  electric  field  drawn  in 
between  the  two  plates  or  driven  out  from  between  them  ? 
Is  the  bound  charge  increased  or  diminished  upon  the  second 
plate  ?  Are  the  bound  charges  upon  distant  conductors 
increased  or  diminished  ?  How  can  you  tell  ? 


FIG.  72. 

Electric  Condensers. — An  arrangement  of  conduct- 
ors by  means  of  which  the  field  of  an  electrified  body 
is  confined  to  a  small  region  of  the  dielectric  is  called 
a  Condenser.  Can  you  make  the  two  plates  serve  as  a 
condenser  ?  How  can  you  screen  an  unelectrified  body 
from  the  influence  of  an  electrified  body  near  it  ? 

The  Electric  Field  of  the  Leyden  Jar.— The  Leyden 
Jar  is  made  by  coating  the  inside  and  outside  of  an 
insulating  glass  jar  with  tin-foil  (which  is  pasted  to  the 
glass),  to  about  one  half  the  height  of  the  jar.  To 
improve  the  insulation  of  the  glass  above  the  tin-foil  it 
is  usually  thinly  coated  with  shellac  from  an  alcohol 
solution.  A  wire  with  a  knob  at  the  top  is  passed 
through  a  wooden  cover,  and  by  means  of  a  piece  of 
chain  or  fine  wire  is  brought  in  contact  with  the  inner 
coating  of  tin-foil.  The  jar  is  electrified  by  bringing 
the  knob  in  contact  with  the  discharging  knob  of  an 


MAGNETISM  AND  ELECTRICITY 


261 


electric  machine  while  the  outer  coating  of  the  jar  is  in 
electric  communication  with  the  earth.  The  bound 
charge  is  then  upon  the  outer  coating  of  the  jar,  and 
the  glass  between  the  two  coats  becomes  the  dielectric. 

Energy  of  Electric  Field  in  the  Dielectric. 

LABORATORY  EXERCISE  97. — Take  a  small  glass  beaker  or 
wide-mouthed  bottle  which  is  found  to  insulate  well.  Fill 
it  half  full  of  shot  to  serve  as  the  inner  conductor,  and  stick 
a  nail  in  the  shot  to  receive  the  charge  from  the  electric 
machine.  Hold  the  beaker  tightly  in  the  hand,  being  care- 
ful to  leave  a  large  insulating  surface  above  the  hand.  The 


FIG.  73- 

beaker  is  then  a  condenser  with  the  glass  for  the  dielectric 
and  the  hand  as  the  conductor  upon  which  the  bound  charge 
will  be  held.  Holding  the  beaker  near  the  machine,  allow  a 
few  short  sparks  to  pass  to  the  nail.  Then  touch  the  nail 
with  the  finger  of  the  other  hand.  If  no  effect  is  felt  upon 
touching  the  nail,  pass  more  sparks  to  it  and  try  again. 


262  PHYSICS 

When  a  slight  shock  is  felt  upon  touching  the  nail,  the  con- 
denser is  sufficiently  charged.  Charge  the  condenser  as 
before,  sufficiently  high  to  give  an  appreciable  shock.  Set 
it  upon  a  block  of  paraffin,  as  shown  in  Fig.  73,  remove  the 
hand  from  the  outside  of  the  beaker,  and  then  withdraw  the 
nail.  Why  do  you  feel  no  indications  of  the  discharge  ? 
Have  the  bound  charges  changed  places  in  the  condenser  ? 

Pick  up  the  beaker,  pour  out  the  shot  and  set  it  back  upon 
the  paraffin  block.  Pour  in  as  much  shot  from  another 
vessel,  replace  the  nail,  grasp  the  outside  of  the  beaker 
tightly  in  the  hand  and  touch  the  nail  with  the  other  hand. 
If  you  feel  no  evidence  of  the  discharge,  repeat  the  experi- 
ment, charging  the  shot  more  highly. 

Can  you  show  that  the  energy  of  the  electric  field  is  in  the 
dielectric  and  not  in  the  conductors  ? 

Electric  Field  of  a  Hollow  Conductor. 

LABORATORY  EXERCISE  98. — Set  a  deep  tin  cup,  a  tin  can 
from  which  all  the  rough  edges  have  been  removed,  or  a 
hollow  wire  conductor  such  as  is  often  sold  for  a  fly  trap, 
on  a  block  of  paraffin,  or  suspend  it  by  insulating  strings. 
Attach  two  pith  balls  to  the  ends  of  a  linen  thread  long 
enough  that  they  can  be  suspended  over  the  edge  or  through 
the  meshes  of  the  conductor,  one  hanging  inside  and  one 
outside  and  reaching  nearly  to  the  bottom  of  the  conductor. 
Suspend  the  two  balls  so  that  they  will  rest  against  the  same 
side  of  the  vessel  and  opposite  each  other.  Electrify  the 
conductor  from  the  machine.  Is  there  evidence  of  an  elec- 
tric field  on  the  inside  ?  Hold  another  conductor  in  the 
hand  and  move  it  about  near  the  charged  hollow  conductor 
on  the  outside.  Can  you  change  the  distribution  of  the 
electric  field  on  the  outside  ?  Why  should  there  be  no 
electric  field  on  the  inside  ? 

Try  to  charge  a  metal  ball  attached  to  a  silk  thread  by 
lowering  it  into  the  hollow  conductor  and  allowing  it  to 
touch  the  side  near  the  bottom.  Can  you  charge  a  body  by 
contact  when  it  is  not  in  an  electric  field  ? 

Discharge  the  hollow  conductor  and  lower  a  charged  metal 
ball  attached  to  a  silk  thread  into  it,  taking  care  that  the 
charged  ball  does  not  touch  the  sides  of  the  hollow  con- 
ductor (see  Fig.  74).  Is  there  now  an  electric  field  inside  the 
hollow  conductor  ?  Is  there  an  electric  field  on  the  outside  ? 


MAGNETISM  AND  ELECTRICITY 


263 


Where  is  the  bound  charge  induced  by  the  charged  ball  ? 
To  what  is  the  field  on  the  outside  of  the  hollow  conductor 
due  ?  If  the  ball  is  positively  charged,  what  is  the  character 
of  the  charge  on  the  outside  of  the  hollow  conductor  ? 
Touch  with  the  finger  the  outside  of  the  hollow  conductor. 


FIG.  74. 

Can  you  destroy  its  electric  field  on  the  outside  ?  Is  there 
still  an  electric  field  on  the  inside  ? 

Withdraw  the  charged  ball  without  allowing  it  to  touch 
the  outer  conductor.  Does  the  hollow  conductor  now  have 
a  field  on  its  outside  ?  What  is  the  nature  of  its  electrifica- 
tion ?  To  what  is  it  due  ? 

Discharge  the  hollow  conductor  and  lower  the  charged 
ball  into  it  again.  Does  the  electric  field  appear  again  upon 
the  outside  ? 

Let   the   charged  ball   come  in  contact  with  the   hollow 


264  PHYSICS 

conductor  on  the  inside.  Which  electric  field  now  dis- 
appears ?  Tell  by  observing  the  attached  pith  ball  if  there 
is  any  noticeable  change  in  the  strength  of  the  outside  field. 

Withdraw  the  ball  and  test  it  for  electrification.  Where 
is  the  electric  field  which  was  around  the  ball  when  it  was 
lowered  into  the  hollow  conductor  ?  Is  the  field  apparently 
of  the  same  strength  as  when  it  belonged  to  the  ball  ? 

Was  the  bound  charge  in  the  inside  of  the  hollow  con- 
ductor exactly  equal  in  magnitude  to  the  inducing  charge 
upon  the  ball  ?  How  can  you  tell  ?  Where  is  now  the 
bound  charge  ? 

How  can  you  make  one  conductor  give  up  its  entire 
charge  to  another  ? 

The  pith  balls  which  you  have  used  for  the  detection  of 
electrification  are  often  called  electroscopes,  that  is,  electric 
indicators.  Much  more  sensitive  electroscopes  may  be 
devised,  but  the  most  sensitive  electroscope  attached  to  the 
hollow  conductor  fails  to  show  any  change  in  its  electrical 
field  when  the  charged  ball  on  the  inside  is  allowed  to  touch 
it. 

Mapping  the  Lines  of  Electric  Force. — The  Electric 
Field,  like  the  Magnetic  Field,  may  be  mapped  out  by 
using  particles  of  some  feebly  conducting  substance 
instead  of  the  iron  filings  used  in  the  magnetic  field. 
The  experiment  would  better  be  performed  by  the 
teacher. 

Pour  enough  turpentine  oil  in  a  flat-bottomed  glass 
vessel  to  cover  the  bottom  to  a  depth  of  half  a  centi- 
meter. Place  two  pieces  of  metal  at  a  distance  of 
eight  or  ten  centimeters  apart  in  the  oil,  and  connect 
them  to  the  knobs  of  the  electric  machine.  Let  one 
person  turn  the  machine  slowly,  not  fast  enough  to 
cause  currents  in  the  liquid,  while  another  holds  a  piece 
of  colored  crayon  above  the  liquid  and  files  off  coarse 
particles  with  a  rough  file.  By  turning  the  machine  at 
the  proper  rate  and  distributing  the  particles  evenly  in 
the  liquid" they  will  form  connecting  lines  between  the 


MAGNETISM  AND  ELECTRICITY  265 

two  pieces  of  metal  like  the  lines  of  iron  filings  between 
the  magnetic  poles.  In  this  case,  the  chalk  filings  are 
turned  into  position  by  the  attraction  between  their 
induced  charges. 

Fig.  75  is  made  by  mapping  an  electric  field  with 
chalk  filings  in  a  glass  vessel  standing  on  a  photographic 
plate  in  a  dark  room.  After  the  machine  was  discon- 
nected, a  lighted  match  was  held  above  the  vessel, 
causing  its  shadow  to  be  projected  upon  the  photo- 
graphic plate  and  the  plate  was  developed. 

The  round  spots  show  the  position  of  the  metal 
cylinders  which  were  connected  to  the  knobs  of  the 
electric  machine,  and  the  rectangular  dark  spot  shows 
the  position  of  a  piece  of  brass  which  was  placed  in  the 
liquid  but  was  not  connected  with  the  electric  machine. 

Compare  with  the  map  of  a  magnetic  field  in  which 
a  piece  of  iron  is  placed  near  the  magnetic  poles. 

Electric  Potential. — On  page  44  we  used  the  term 
"  Potential  "  of  a  point  in  space  to  indicate  the  poten- 
tial energy  which  a  unit  mass  would  have  at  that  point 
on  account  of  gravitation.  Since  two  electrified  bodies 
brought  near  each  other  have  potential  energy  on 
account  of  the  electric  pressure  tending  to  separate 
them  or  bring  them  together,  we  may  calculate  the 
electric  potential  of  a  point  in  space  as  well  as  its  gravi- 
tation potential.  If  we  agree  upon  a  unit  quantity  of 
electrification,  we  may  say  that  the  electric  potential 
of  a  point  in  space  is  the  measure  of  the  potential 
energy  which  the  unit  quantity  of  electrification  would 
have  at  that  point.  In  this  view,  what  we  have  called 
the  electric  pressure  corresponds  to  the  gravitation 
pressure  or  the  weight  of  the  unit  mass  in  gravitation 
potential. 


266 


PHYSICS 


FIG.  75- 


MAGNETISM  AND  ELECTRICITY  267 

Since  a  positively  electrified  body  will  be  driven  in 
one  direction  in  an  electric  field  and  a  negatively 
electrified  body  will  be  driven  in  the  opposite  direction, 
a  point  in  an  electric  field  may  have  a  different  potential 
for  the  two  kinds  of  electrification.  It  is  accordingly 
customary  to  regard  the  electric  potential  of  a  point  as 
the  potential  energy  which  the  unit  quantity  of  positive 
electrification  would  have  at  the  point  due  to  the  repul- 
sion of  the  electric  field  upon  it. 

Since  a  positively  electrified  body  would  not  be 
repelled  in  the  field  of  a  negatively  electrified  body  it 
would  have  no  potential  energy  due  to  repulsion  in  such 
a  field,  but  would  require  the  expenditure  of  work  upon 
it  to  carry  it  away  from  the  negatively  electrified  body ; 
hence  its  potential  is  said  to  be  negative. 

Zero  Potential. — Since  all  electrified  bodies  lose 
their  electrification  on  contact  with  the  earth,  the  earth 
is  regarded  as  unelectrified,  and  hence  at  zero  potential. 

Potential  Difference. — It  is  sometimes  possible  to 
calculate  the  electric  potential  of  a  point  in  space,  but 
the  problem  is  principally  of  mathematical  interest. 
What  we  generally  wish  to  know  in  practice  is  the 
potential  difference  between  two  points.  The  potential 
difference  of  two  points  is  the  measure  of  the  work 
which  must  be  done  on  a  body  charged  with  the  unit 
quantity  of  positive  electrification  to  carry  it  from  the 
one  point  to  the  other. 

Since  work  is  measured  by  force  into  distance,  or 
W=  FS,  the  potential  difference  between  two  points 
will  be  greater  the  greater  the  electric  force  between 
them.  Thus  if  V  -  V  represent  the  potential  differ- 
ence between  two  points  and  S  the  distance  between 


268  PHYSICS 

V  —  V 
them, ~ =  F,  where  F  is  the  average  electric 

force  between  the  points.  The  average  electric  force 
between  two  points  is  accordingly  the  change  of  poten- 
tial per  unit  distance  between  the  two  points. 

Electromotive  Force.  —  Electromotive  Force  is  a 
name  given  to  whatever  tends  to  move  an  electric 
charge.  In  the  proper  sense  it  is  not  a  force  at  all, 
because  force  has  been  defined  since  the  time  of 
Newton  as  whatever  produces  or  tends  to  produce  an 
acceleration  in  a  material  body.  An  electromotive 
force  does  not  affect  a  material  body  at  all,  hence 
cannot  produce  an  acceleration  in  such  a  body.  It 
does,  however,  produce  an  acceleration  of  an  electric 
quantity,  and  hence  is  analogous  to  a  force,  just  as  the 
electric  elasticity  of  a  dielectric  is  analogous  to  the 
elasticity  of  a  material  body. 

The  best-known  form  of  electromotive  force  is  the 
pressure  which  is  exerted  upon  an  electric  charge  in 
an  electric  field.  This  form  of  electromotive  force  may 
be  measured,  as  above,  by  the  potential  difference 
between  the  two  charges  divided  by  their  distance; 

V '—  V 
that  is,  E.M  F.  =  ^ . 

ELECTRIC   QUANTITY 

Definition  of  Unit  Quantity. — We  have  spoken  of  a 
unit  quantity  of  electrification,  but  have  not  defined  it. 
It  has  been  defined  as  the  quantity  which  at  a  distance 
of  one  centimeter  from  a  similar  and  equal  quantity 
would  be  acted  upon  by  a  pressure  of  one  dyne.  The 
electrostatic  unit  of  quantity  is  accordingly  very  small, 
and  is  not  used  at  all  in  practical  work. 


MAGNETISM  AND  ELECTRICITY  269 


ELECTRIC   CAPACITY 

Definition  of  Electric  Capacity. — When  two  electri- 
fied conductors  come  in  contact  with  each  other  the 
electric  pressure  becomes  the  same  over  the  surface  of 
both.  Since  there  is  no  difference  of  electric  pressure 
between  the  two  bodies,  there  can  be  no  difference  of 
potential  between  two  points  on  their  surfaces,  hence 
the  bodies  are  said  to  be  charged  to  the  same  potential. 

We  have  seen  that  a  small  body,  as  a  pith  ball,  may 
be  charged  by  contact  to  the  same  potential  as  a  larger 
body  without  appreciably  decreasing  the  electrification 
of  the  larger  body.  We  accordingly  see  that  different 
quantities  of  electrification  may  be  required  to  charge 
different  conductors  to  the  same  potential.  This  is 
expressed  by  saying  that  different  conductors  have 
different  electrical  capacities.  A  large  sphere  has  a 
greater  capacity  than  a  small  sphere.  The  capacity  of 
a  conductor  is  measured  by  the  quantity  of  the  charge 
which  must  be  given  to  it  to  raise  its  potential  from 
zero  to  unity.  Thus  if  C  stand  for  capacity,  Q  for 
quantity  of  charge,  and  V  for  potential,  (7F=  Q. 

Capacity  of  a  Condenser. 

LABORATORY  EXERCISE  99. — Set  a  Leyden  Jar  upon  a  block 
of  paraffin  or  other  insulating  support  and  connect  its  knob 
to  one  knob  of  the  electric  machine.  Separate  the  knobs  of 
the  machine  a  few  millimeters  and  turn  the  handle,  noting 
the  time  between  the  sparks.  When  the  difference  of  poten- 
tial between  the  knobs  becomes  great  enough,  the  dielectric 
between  them  is  broken  through  and  the  knobs  are  dis- 
charged by  a  spark.  For  the  purpose  of  the  present  experi- 
ment, it  may  be  assumed  that  the  "  Electric  Strength  '  of 
the  dielectric  is  constant,  and  that  a  spark  will  pass  under 
the  same  difference  of  potential  each  time.  Does  this  seem 
to  be  approximately  true  ? 


2  70  PHYSICS 

Now  remove  the  insulating  block,  or  connect  the  outer 
coating  of  the  Leyden  Jar  to  earth  by  a  conductor,  and  turn 
the  machine  at  the  same  rate  as  before.  What  effect  does 
this  have  upon  the  time  between  sparks  ?  What  effect  upon 
the  character  of  the  spark  ?  What  effect  has  connecting  the 
outer  coating  of  the  jar  to  earth  had  upon  the  electrical 
capacity  of  the  inner  coating  of  the  jar  ? 

SPECIFIC   INDUCTIVE   CAPACITY 

Experiment  on  Specific  Inductive  Capacity  of 
Paraffin. 

LABORATORY  EXERCISE  100. — Two  metal  discs  are  con- 
nected by  a  conducting  rod,  and  are  mounted  upon  an 
insulating  support.  One  of  the  discs  is  provided  with  a  pith- 
ball  pendulum  to  serve  as  an  electroscope. 

Two  other  metal  discs  of  the  same  size  as  those  mounted 
upon  the  rod  are  placed  at  a  distance  of  an  inch  or  two  from 
the  first  ones,  and  are  mounted  upon  conducting  supports  or 
connected  to  earth.* 

Charge  the  insulated  discs  until  the  pendulum  stands  out 
as  shown  in  Fig.  76.  You  now  have  two  similar  condensers 
at  the  ends  of  the  insulated  rod.  Support  a  block  of  paraffin 
as  large  as  the  discs  and  of  a  thickness  nearly  equal  to  the 
distance  between  the  condenser  plates  by  a  narrow  silk 
ribbon  or  thread  attached  to  two  of  its  corners,  and  after 
passing  the  hand  over  its  faces  to  remove  any  charge  which 
may  be  on  them  lower  it  into  one  of  the  condensers  as  shown 
in  the  figure,  meanwhile  noticing  the  movement  of  the  pith- 
ball  pendulum  in  the  other  condenser.  Withdraw  the  paraffin 
block,  and  repeat  the  experiment  until  you  are  certain 
what  effect  its  introduction  has  on  the  other  condenser. 

Discharge  the  condensers  and  introduce  the  paraffin  as 
before  to  determine  whether  it  carries  an  electric  charge.  If 
it  is  found  to  be  charged,  discharge  it  by  passing  it  quickly 
through  a  flame,  and  when  it  is  completely  discharged  repeat 
the  whole  experiment. 

Since  the  insulated  discs  of  the  condensers  are  joined  by 

*  A  tin  can,  as  a  baking-powder  can,  mounted  upon  insulating  sup- 
ports may  take  the  place  of  the  rod  and  discs,  and  two  other  can  covers 
mounted  upon  wooden  supports  may  serve  for  the  movable  discs. 


MAGNETISM  AND  ELECTRICITY 


271 


a  conductor,  they  must  remain  always  at  the  same  potential. 
Since  the  other  discs  are  joined  to  earth,  they  must  be  always 
at  zero  potential.  The  potential  difference  in  the  two  con- 
densers must  accordingly  remain  the  same  throughout  the 
experiment. 

Is  this   potential  difference   increased    or  diminished  by 
the  introduction  of  the  paraffin  ?     (If  it  is  increased,  the 


FIG.  76. 

electric  field  in  both  condensers  is  strengthened,  and  the  pith 
ball  is  more  strongly  electrified  than  before.) 

When  the  paraffin  is  introduced,  must  the  charge  of  the 
insulated  discs  be  increased  or  diminished  to  restore  the 
previous  strength  of  field  in  the  condensers  ? 

Is  the  capacity  of  the  paraffin  condenser  greater  or  less 
than  that  of  the  air  condenser  ? 

Is  the  introduction  of  the  paraffin  equivalent  to  separating 
the  plates  or  to  bringing  them  together  ?  Try  the  experiment. 

Is  the  bound  charge  induced  through  paraffin  greater  or 
less  than  that  induced  through  the  same  thickness  of  air  ? 

Definition  of  Specific  Inductive  Capacity. — The  fact 
that  electric  induction  takes  place  more  readily  through 
some  dielectrics  than  through  others  was  discovered 
by  Faraday,  who  gave  the  name  Specific  Inductive 
Capacity  to  that  property  of  dielectrics  by  means  of 
which  induction  is  produced.  Substances  through 
which  induction  takes  place  easily  are  said  to  have  a 


2  72  PHYSICS 

high  specific  inductive  capacity,  or  a  high  "  Dielectric 
Capacity. ' '  The  specific  inductive  capacity  of  a  con- 
ductor is  so  great  that  induction  takes  place  through  it 
as  readily  as  if  the  condenser  plates  were  moved  nearer 
together  by  the  thickness  of  the  conductor. 

Relation  of  Specific  Inductive  Capacity  to  Electric 
Elasticity. — We  have  seen  that  increasing  the  specific 
inductive  capacity  of  the  dielectric  between  a  charged 
body  and  its  bound  charge  increases  the  magnitude  of 
the  bound  charge,  and  in  this  respect  is  equivalent  to 
bringing  the  conductors  nearer  together.  We  saw  in 
the  experiment  on  the  capacity  of  the  Leyden  Jar  that 
bringing  a  bound  charge  nearer  to  a  charged  conductor 
had  the  effect  of  lowering  the  electric  pressure  upon 
the  surface  of  the  charged  conductor.  It  follows  that 
increasing  the  specific  inductive  capacity  of  the  dielec- 
tric in  the  field  of  a  charged  conductor  must  lower  the 
electric  pressure  upon  the  surface  of  the  conductor. 

We  have  assumed  that  this  electric  pressure  is  due 
to  the  Electric  Elasticity  of  the  dielectric.  Since  elas- 
ticity is  measured  by  the  resistance  which  a  body  offers 
to  pressure,  the  electric  elasticity  of  the  dielectric  is 
measured  by  the  electric  pressure  which  it  exerts.  If 
increasing  the  specific  inductive  capacity  of  the  dielec- 
tric lowers  the  electric  pressure  upon  a  charged  body, 
it  must  be  that  it  decreases  the  electric  elasticity  of  the 
dielectric. 

A  conductor  immersed  in  paraffin  will  require  about 
twice  the  electrical  quantity  to  charge  it  so  that  it  will 
have  a  given  electrical  pressure  upon  its  surface  that  it 
would  if  it  were  in  air.  In  alcohol,  which  has  a  specific 
inductive  capacity  twenty-five  times  as  great  as  air,  a 
conductor  will  require  twenty- five  times  the  electrical 


MAGNETISM  AND  ELECTRICITY  273 

quantity  to  produce  a  given  electrical  pressure  that  it 
will  in  air.  It  follows  that  what  we  have  called  the 
electric  elasticity  is  about  one  half  as  great  in  paraffin 
and  about  one  twenty-fifth  as  great  in  alcohol  as  in  air. 
If  the  Luminiferous  Ether  is  the  medium  by  which 
electrical  pressures  are  transmitted,  the  electric  elas- 
ticity of  the  Ether  must  be  different  when  it  is  associated 
with  different' kinds  of  matter.  All  known  bodies  have 
greater  specific  inductive  capacities  than  the  vacuum, 
hence  the  electric  elasticity  of  the  Ether  is  apparently 
diminished  when  it  is  associated  with  any  kind  of 
matter. 

ELECTRIC    DISCHARGE 

Discharge  of  Electrification  from  a  Pointed  Con- 
ductor. 

LABORATORY  EXERCISE  101. — Provide  an  insulated  con- 
ductor with  a  needle  point  and  with  a  pith-ball  electroscope 
attached  at  some  distance  from  the  point. 

Will  such  a  conductor  retain  its  electrification  when 
charged  ? 

Hold  a  candle  flame  near  the  point  while  the  conductor 
is  being  charged  from  the  machine.  Do  you  find  indications 
that  electrified  particles  are  being  repelled  from  the  point  ? 

Why  should  all  the  conductors  in  the  preceding  experi- 
ments have  smooth  surfaces  ? 

Electrify  an  insulated  conductor  and  hold  near  it  an  un- 
insulated conductor  provided  with  a  point.  Does  the  bound 
charge  send  off  electrified  particles  to  the  charged  conductor  ? 

How  would  such  particles  affect  the  electrification  of  the 
charged  conductor  ? 

The  Spark  Discharge. — We  have  seen  that  when 
the  electric  pressure  between  the  knobs  of  the  electric 
machine  becomes  great  enough  a  spark  will  pass 
between  the  knobs,  and  the  opposite  electrifications  of 
the  two  knobs  will  disappear.  Just  what  takes  place 
at  the  time  of  the  discharge  to  cause  the  spark  and  the 


274  PHYSICS 

equalization  of  the  electric  condition  of  the  conductors 
is  not  known.  We  can  learn  of  the  conditions  pro- 
duced in  the  dielectric  and  the  conductors  by  the  dis- 
charge, but  we  do  not  know  what  is  discharged.*  We 
know  that  it  requires  the  expenditure  of  energy  to 
produce  an  electric  field.  The  crank  of  the  electric 
machine  is  more  easily  turned  when  the  discharging 
knobs  are  in  contact  than  when  they  are  separated  and 
an  electric  field  is  being  formed  between  them.  It 
requires  more  work  to  separate  the  flannel  and  sealing 
wax  after  they  have  become  electrified  than  before. 
This  work  is  represented  by  the  potential  energy  of  the 
field,  which  seems  analogous  to  the  potential  energy  of 
a  displacement  produced  in  an  elastic  body,  such  as 
the  bending  of  a  spring,  the  stretching  of  a  rubber 
membrane,  or  something  of  a  similar  nature.  The 
discharge  of  the  electrification  is  like  setting  free  the 
spring  or  membrane,  and  the  potential  energy  of  the 
charge  is  changed  again  into  kinetic  energy.  If  the 
discharge  takes  place  through  a  long,  thin  conductor, 
the  conductor  is  heated.  If  it  takes  place  through  the 
dielectric,  the  dielectric  is  heated;  and  by  whatever 
process  it  takes  place  work  is  performed.  If  a  card  be 
held  between  the  discharging  knobs,  it  is  perforated  by 
the  discharge.  A  piece  of  paper  dipped  in  a  solution 
of  potassic  iodide  and  starch  shows  that  iodine  is  set 
free  by  the  electric  spark.  Thus  the  energy  of  fche 
discharge  may  be  used  in  doing  mechanical  work,  in 
producing  a  chemical  change,  and  in  generating  heat. 
Instantaneous  Character  of  Spark  Discharge. — The 
instantaneous  character  of  the  electric  discharge  may 

*  It  seems  extremely  probable  that  the  electrical  charges  transferred 
in  the  spark  discharge  are  carried  by  the  electrons  referred  to  in  the 
foot-note  on  page  165. 


MAGNETISM  AND  ELECTRICITY  275 

be  shown  by  illuminating  with  the  spark  a  rapidly 
moving  object,  as  a  rotating  wheel.  The  short  dura- 
tion of  the  illumination  causes  the  moving  object  to 
appear  at  rest. 

Oscillatory  Character  of  Spark  Discharge. — If  the 
image  of  the  electric  spark  be  observed  in  a  very  rapidly 
rotating  mirror,  it  will  be  seen  to  consist  of  several  suc- 
cessive sparks.  The  greater  the  capacity  of  the  dis- 
charging conductor,  the  farther  apart  will  these  sparks 
appear.  The  images  of  these  successive  sparks  have 
been  projected  and  photographed  by  means  of  a  rapidly 
rotating  concave  mirror.  They  are  explained  by 
supposing  a  discharge  to  take  place  back  and  forth 
between  the  discharging  knobs. 

Fall  of  Potential  in  Electric  Conduction. 

LABORATORY  EXERCISE  102. — Suspend  a  smooth  wooden 
rod  two  or  three  meters  long  by  silk  threads,  and  provide  it 
with  several  pith-ball  or  paper  electroscopes  distributed  at 
equal  distances  along  the  rod.  Connect  one  end  of  the  rod 
by  a  wire  to  a  gas  or  water  pipe,  and  connect  the  other  end 
to  one  discharging  knob  of  the  electric  machine,  and  elec- 
trify the  rod  as  highly  as  possible. 

Does  electrification  pass  through  the  wood  ?  Is  the  rod 
equally  electrified  throughout  its  entire  length  ?  If  not, 
where  is  the  electrical  pressure  upon  the  surface  of  the  rod 
greatest  ?  Where  is  the  electric  potential  in  the  air  near  the 
rod  greatest  ? 

Connect  the  same  knob  of  the  machine  to  the  same  place 
on  the  steam  or  water  pipe  by  a  copper  wire.  Which  carries 
off  the  charge  from  the  machine  the  quicker,  the  rod  or  the 
wire  ? 

Which  seems  to  offer  the  greater  resistance  to  the  passage 
of  the  electric  charge  ? 

Remove  the  wire  from  the  knob  of  the  electric  machine, 
disconnect  the  rod  from  the  earth  and  connect  its  ends  to 
the  two  knobs  of  the  machine  as  in  Fig.  77,  and  again  elec- 
trify it  as  highly  as  possible.  Where  are  the  pith  balls  now 


276  PHYSICS 

most  strongly  electrified  ?  Can  you  find  a  place  on  the  rod 
where  a  pith  ball  shows  no  electrification  ?  Is  such  a  place 
at  the  same  electric  potential  as  the  earth  ?  Connect  such 
a  place  to  the  earth  through  the  steam  or  water  pipe.  Is 
the  difference  of  electric  potential  of  the  two  ends  of  the  rod 
apparently  greater  or  less  than  between  either  end  and  the 
earth  ?  If  the  earth  be  taken  as  at  zero  potential,  give 


FIG.  77- 

reasons  for  saying  that  one  end  of  the  rod  is  at  a  positive 
potential  and  the  other  at  a  negative  potential. 

If  there  is  only  one  kind  of  electrification,  give  reasons  for 
saying  that  a  body  may  be  more  or  less  highly  charged  than 
the  earth. 

ELECTRIFICATION  OF  THE  EARTH 
The  Earth's  Electric  Field. — We  have  seen  reasons 
in  the  preceding  experiment  for  believing  that  the 
earth  itself  is  highly  electrified,  so  that  of  the  two 
electrical  conditions,  the  positive  and  the  negative,  the 
one  represents  a  higher  degree  of  electrification  than 
the  earth,  and  the  other  a  lower.  Since  no  limit  has 
been  found  to  the  possible  intensity  of  either  positive  or 
negative  electrification,  no  such  thing  as  a  total  absence 
of  electrification  is  known,  and  the  absolute  intensity 
of  the  earth's  electrification  cannot  be  measured. 


MAGNETISM  AND  ELECTRICITY        -  277 

Electrification  of  the  Air. — The  first  observations 
on  the  electrification  of  the  air  above  the  earth  were 
made  by  Benjamin  Franklin  in  his  celebrated  kite 
experiment.  Franklin  was  familiar  with  the  method 
of  discharging  insulated  conductors  by  holding  a  pointed 
conductor  near  them,  and  he  conceived  the  idea  of 
"  drawing  off"  the  electrification  of  a  thunder  cloud  in 
the  same  way.  By  means  of  a  kite  provided  with 
metallic  points  and  attached  to  a  moistened  string  held 
by  a  silk  ribbon  at  the  end,  he  was  able  to  take  sparks 
from  a  key  suspended  at  the  end  of  the  string.  Franklin 
thought  of  this  as  drawing  off  the  electricity  of  the 
cloud.  We  think  of  it  as  charging  the  key  by  induc- 
tion, the  "bound  charge  "  in  this  case  escaping  from 
the  points  on  the  kite. 

Since  Franklin's  time  many  methods  of  finding  the 
electric  pressure  at  a  point  in  the  atmosphere  have  been 
tried.  In  one  of  the  methods  devised  by  Lord  Kelvin 
an  insulated  vessel  of  water  is  raised  to  the  desired 
height  and  is  connected  by  a  wire  to  an  electroscope 
which  is  at  the  electrical  pressure  of  the  earth.  Water 
is  then  allowed  to  fall  in  drops  from  the  insulated  vessel. 
Since  the  vessel  of  water  is  charged  to  the  electric 
pressure  of  the  earth  while  the  dielectric  in  its  vicinity 
is  charged  to  a  lower  pressure,  each,  drop  of  water  will 
carry  off  some  of  the  charge  of  the  vessel  and  the  elec- 
troscope until  these  are  at  the  same  electric  pressure 
as  the  point  from  which  the  drops  fall.  By  testing  the 
electrification  of  the  electroscope  the  desired  electrical 
condition  of  this  point  may  be  known. 

While  the  electrification  at  the  same  point  in  the 
atmosphere  varies  greatly  from  day  to  day,  and  while 
the  change  in  electric  pressure  for  a  given  elevation  is 


278  PHYSICS 

very  different  over  different  points  of  the  earth,  in 
general  a  point  taken  anywhere  above  the  earth  is 
positively  electrified  with  reference  to  the  earth. 

Electrification  of  Clouds. — The  small  dust  particles 
which  form  the  nuclei  of  rain  drops  (see  page  165)  have 
floated  about  in  the  atmosphere  until  they  have  gen- 
erally taken  an  electrical  condition  different  from  that 
of  the  earth.  When  condensation  takes  place  upon 
them,  the  water  drops  thus  formed  take  the  electrical 
condition  of  the  dust  particles.  As  they  settle  into  a 
region  of  different  electrical  pressure  they  are  charged 
with  reference  to  the  surrounding  dielectric.  When 
two  of  them  combine,  the  resulting  drop  takes  the 
charge  of  both  its  constituent  drops.  The  new  sphere 
of  water  thus  formed  has  accordingly  twice  the  electric 
charge  of  either  constituent  sphere  (assuming  these  to 
be  equally  charged),  but  has  not  twice  the  capacity  of 
either  of  them.  The  electric  capacity  of  a  sphere 
increases  in  proportion  to  its  radius.  The  radius  of  a 
sphere  is  not  doubled  when  its  volume  is  doubled. 
Hence  the  electric  pressure  at  the  surface  of  the  new 
drop  is  greater  than  at  the  surface  of  its  constituent 
drops.  By  the  combination  of  many  small  rain  drops 
into  larger  ones,  the  electric  pressure  upon  the  drops 
may  become  very  great.  This,  together  with  the  fact 
that  the  drops  are  constantly  settling  into  a  region  of 
different  electric  pressure,  may  account  for  the  very  high 
pressures  sometimes  observed  in  thunder  clouds.* 

*  It  is  also  known  that  the  negative  electrons  (see  p.  165)  which  are 
formed  by  the  breaking  up  of  the  gas  atom  are  especially  adapted  to 
forming  nuclei  for  the  condensation  of  water  drops.  Drops  formed 
about  such  nuclei  are  negatively  charged,  and  when  two  such  drops 
combine  the  resultant  charge  is  the  sum  of  the  two  original  charges. 
Its  electric  pressure  is  accordingly  increased  in  the  manner  mentioned 


MAGNETISM  AND  ELECTRICITY  279 

When  these  highly  charged  clouds  approach  the 
earth  they  induce  bound  charges  upon  the  parts  of  the 
earth  nearest  to  them.  This  changes  the  distribution 
of  the  electric  field  about  the  cloud,  and  when  the 
pressure  becomes  great  enough  a  disruptive  discharge 
takes  place  between  the  cloud  and  the  earth,  or 
between  two  clouds  whose  nearest  points  are  in  oppo- 
site electrical  conditions.  This  discharge,  which  we 
call  Lightning,  often  takes  place  through  great  thick- 
nesses of  air,  but  generally  from  one  conducting  particle 
to  another,  and  not  in  a  straight  line. 

Protection  from  Lightning. — Franklin  was  the  first 
to  suggest  the  use  of  long,  pointed  conductors  con- 
nected to  earth  and  projecting  above  buildings  to 
"  draw  off"  the  charge  from  adjacent  clouds  and  pre- 
vent a  disruptive  discharge  to  the  building.  As  we 
now  know,  the  purpose  served  by  the  lightning  rod  is 
to  prevent  the  formation  of  a  bound  charge  on  the 
building.  Formerly,  lightning  rods  were  carefully 
insulated  from  buildings,  but  we  now  understand  that 
they  are  more  effective  if  in  metallic  contact  with  the 
conducting  parts  of  the  building. 

Since  the  purpose  of  the  point  is  to  facilitate  the 
escape  of  the  bound  charge,  it  should  be  kept  sharp, 
and  should  be  made  of  some  metal  not  easily  corroded 
by  the  action  of  the  atmosphere. 

From  what  we  have  seen  of  the  impossibility  of  an 
electric  field  within  a  hollow  conductor,  it  follows  that 
the  most  efficient  protection  from  lightning  would  be  a 

above.  Such  drops  form  negatively  electrified  clouds,  and  when  they 
fall  to  the  earth  they  leave  the  upper  air,  which  still  contains  the  electro- 
positive parts  of  the  atoms  positively  electrified.  It  is  believed  by  many 
physicists  that  these  electrons  play  a  very  important  part  in  the  electri- 
fication of  the  air. 


280  PHYSICS 

conducting  covering,  such  as  a  netting  of  wire,  joined 
to  the  earth. 

CURRENT   ELECTRICITY 

THE   VOLTAIC   CELL 

Displacement  of  One  Metal  by  Another  in  an  Acid 
Solution. 

LABORATORY  EXERCISE  103. — Prepare  a  solution  of  copper 
sulphate  in  water  in  a  tumbler  or  beaker,  and  place  a  bright 
piece  of  iron  or  steel  in  it  for  a  few  minutes.  What  evidence 
have  you  that  the  copper  sulphate  has  been  decomposed  ? 

Repeat,  using  a  strip  of  zinc,  instead  of  iron.  Is  copper 
separated  from  the  solution  ?  Does  zinc  go  into  the  solu- 
tion ? 

Put  two  strips  of  zinc  and  one  strip  of  copper  in  a  vessel 
of  the  solution,  putting  one  strip  of  the  zinc  in  contact  with 
the  copper  strip,  and  leaving  the  other  zinc  strip  separated 
from  both  the  other  metal  strips.  Upon  which  zinc  strip  is 
the  copper  deposited  the  more  rapidly  ?  Does  the  other  zinc 
strip  go  into  solution  ? 

Pour  a  little  sulphuric  acid  into  a  vessel  of  water  and  dip 
strips  of  copper  and  amalgamated*  zinc  into  it  separately. 
If  the  metal  goes  into  solution  it  drives  out  hydrogen  gas, 
which  can  be  seen  as  bubbles  upon  the  surface  of  the  metal. 

Which  metal  seems  to  go  into  solution  the  more  readily  r 
Try  a  strip  of  the  zinc  which  has  not  been  amalgamated. 

Put  the  copper  and  amalgamated  zinc  into  the  solution 
together,  making  a  metallic  contact  between  them  by  touch- 
ing them  together  or  by  connecting  them  by  means  of  a 
copper  wire.  What  difference  do  you  observe  in  the  action 
of  the  acid  upon  the  two  metals  ? 

Formation  of  Ions  in  the  Solution. — When  a  metal 
dissolves  in  an  acid,  the  molecules  or  parts  of  molecules 

*  The  zinc  is  amalgamated  by  first  cleaning  it  and  then  dipping  it 
into  a  vessel  containing  a  little  mercury  and  some  dilute  sulphuric  acid 
and  while  the  zinc  is  in  the  liquid  rubbing  the  mercury  over  it  by  means 
of  a  brush  or  a  rag  tied  on  a  stick.  When  the  zinc  shows  a  bright  coat- 
ing of  mercury  it  should  be  washed  in  water  and  is  then  ready  for  use. 


MAGNETISM  AND  ELECTRICITY  281 

which  go  into  the  solution  are  called  Ions.  These  ions 
always  drive  out  other  ions  of  the  solution.  The  ions 
which  are  driven  out  of  ordinary  acids  by  the  solution 
of  metals  are  hydrogen.  In  the  copper  sulphate  solu- 
tion copper  ions  were  driven  out  by  the  iron  or  zinc. 

Positive  Charges  of  Metallic  Ions. — It  has  been 
found  by  the  use  of  very  sensitive  electroscopes  that 
when  metallic  ions  are  dissolved  off  a  metal  plate  in  an 
acid  solution  they  carry  with  them  positive  electric 
charges,  and  leave  the  metal  plate  negatively  electri- 
fied. 

Differences  in  Electrical  Conditions  of  Different 
Metals  in  the  Same  Solution. — If  two  metal  plates, 
one  of  which  dissolves  in  the  acid  while  the  other  does 
not  (as  zinc  and  platinum)  be  put  into  an  acid  solution, 
the  plate  which  dissolves  becomes  electro-negative  to 
the  other.  If  both  plates  dissolve  in  the  acid,  the 
plate  which  dissolves  the  more  rapidly  becomes  elec- 
tro-negative to  the  other. 

Production  of  the  Electric  Current.— If  the  plates 
be  connected  by  a  conductor  they  necessarily  acquire 
the  same  potential,  and  the  ions  which  are  driven  out 
of  the  solution  go  to  the  plate  which  dissolves  least. 
Since  the  ions  take  away  positive  charges  from  one 
plate  and  carry  positive  charges  to  the  other,  they  tend 
to  cause  a  difference  in  the  electrical  potential  of  the 
two  plates,  and  this  difference  can  be  neutralized  only 
by  the  passage  of  positive  electricity  along  the  con- 
ductor joining  the  two  plates. 

Thus  with  plates  of  zinc  and  copper  in  copper  sul- 
phate solution,  the  zinc  ions  replace  the  copper  ions  in 
the  solution,  and  the  copper  ions  are  deposited  upon 
the  copper  plate.  The  zinc  plate  is  continually  becom- 


282  PHYSICS 

ing  more  electro-negative  and  the  copper  plate  more 
electro-positive,  and  this  condition  is  neutralized  by  the 
electrical  flow,  called  the  current,  along  the  wire  from 
the  copper  to  the  zinc. 

If  the  plates  be  disconnected,  the  copper  plate  soon 
becomes  so  strongly  electro-positive  that  it  repels  the 
positively  charged  ions  in  the  solution,  and  these  in 
return  repel  the  positive  ions  which  are  leaving  the 
zinc  plate  and  prevent  their  escape  into  the  solution. 
Accordingly,  in  this  condition  the  solution  of  the  zinc 
plate  may  cease  entirely.*  The  plates  are  then  said 
to  be  polarized. 

Construction  of  the  Voltaic  Cell. — The  arrange- 
ment of  the  zinc  and  copper  plates  with  a  dissolving 
liquid  to  give  an  electric  current  is  called  a  Voltaic 
Cell.  Many  other  metals  and  liquids  may  be  used  in 
the  voltaic  cell.  The  zinc  and  copper  combination  is 
frequently  used,  as  is  also  the  combination  of  zinc  and 
carbon  with  a  liquid  which  gives  off  hydrogen  ions 
when  the  zinc  dissolves  in  it.  The  hydrogen  is 
absorbed  by  the  carbon  until  the  carbon  becomes 
saturated  with  it,  after  which  it  rises  in  bubbles  to  the 
surface.  Since  the  difference  of  potential  between  zinc 
and  hydrogen  cannot  become  as  great  as  between  zinc 
and  carbon,  an  oxidizing  substance  of  some  kind  is 
frequently  combined  with  the  carbon,  or  the  carbon  is 
placed  in  a  porous  cup  containing  a  strong  oxidizing 

*  This  is  true  only  when  the  zinc  is  pure.  If  it  contain  iron  or  other 
metals,  the  action  may  go  on  between  different  points  on  the  surface  of 
the  plate,  ions  being  given  off  by  the  zinc  and  other  ions  being  deposited 
upon  the  iron  or  other  metal.  To  prevent  this  action,  the  zincs  used  for 
generating  a  current  are  usually  amalgamated.  The  mercury  dissolves 
the  zinc  and  brings  zinc  ions  to  the  surface  continuously,  while  it  does 
not  dissolve  the  impurities  which  are  electro-positive  to  the  zinc. 


MAGNETISM  AND  ELECTRICITY  283 

agent,  as  nitric   or  chromic   acid,   to  keep  the  carbon 
surface  free  from  hydrogen. 

PROPERTIES    OF   THE    ELECTRIC    CURRENT 
Magnetic  Field  of  the  Current. 

LABORATORY  EXERCISE  104. — In  the  following  exercise  a 
voltaic  cell  giving  a  stronger  current  than  the  zinc  and  copper 
strips  of  the  previous  experiment  should  be  used.  An 
Edison-Lalande  cell,  in  which  zinc  and  copper  oxide  plates 
are  placed  in  a  strong  solution  of  caustic  potash,  is  well 
adapted  to  our  purpose. 

Connect  the  plates  of  the  Edison-Lalande  cell  by  a  piece 
of  rather  coarse,  bare  copper  wire  about  two  feet  long,  and 
dip  the  middle  of  the  wire  into  iron  filings.  What  evidence 
have  you  of  magnetic  action  ? 

N.B.  Always  disconnect  the  wire  from  one  terminal  of  the 
cell  when  not  in  use.  Why  ? 

Lay  a  piece  of  cardboard  on  some  convenient  support, 
make  a  small  hole  through  it,  and  pass  the  copper  wire  from 
the  cell  through  the  hole,  keeping  the  wire  vertical.  Connect 
the  wire  with  the  terminals  of  the  cell  and  scatter  iron  filings 
on  the  cardboard  around  the  wire.  Tap  the  cardboard  until 
the  filings  arrange  themselves  in  lines.  Do  the  lines  of  the 
magnetic  field  radiate  from  the  wire,  or  do  they  circle 
around  it  ? 

Direction  of  the  Lines  of  Magnetic  Force  about  a 

Current. 

By  the  aid  of  a  small,  suspended  magnetic  needle,  deter- 
mine the  positive  direction  of  the  lines  of  magnetic  force  in 
the  field  about  the  current.  Assuming  that  the  current  is 
flowing  along  the  wire  from  the  copper  or  carbon  plate  to 
the  zinc  plate,  look  along  the  wire  in  the  direction  of  the 
current  and  tell  whether  the  magnetic  lines  of  force  are  in 
the  same  direction  or  the  opposite  direction  to  the  motion 
of  the  hands  of  a  watch. 

Take  hold  of  the  wire  with  your  right  hand  with  your 
thumb  pointing  in  the  direction  of  the  current.  Do  your 
fingers  point  in  the  direction  of  the  lines  of  magnetic  force 
or  in  the  opposite  direction  ? 

Bend  the  wire  into  a  loop  without  allowing  it  to  touch 


284  PHYSICS 

where  it  crosses,  and  place  the  magnetic  needle  inside  the 
loop.  Looking  in  the  positive  direction  along  the  lines  of 
magnetic  force,  is  the  direction  of  the  current  around  the 
needle  clockwise  or  counter-clockwise  ? 

Take  hold  of  the  needle  with  one  hand  so  that  your  thumb 
will  point  in  the  positive  direction  of  the  lines  of  magnetic 
force  and  your  fingers  in  the  direction  of  the  current.  Which 
hand  must  you  use  ? 

Give  a  rule  for  determining  the  direction  of  a  current  along 
a  wire  by  means  of  a  magnetic  needle. 

Give  a  rule  for  finding  the  north-seeking  pole  of  a  magnet 
by  means  of  a  wire  carrying  a  current. 

Temperature  Effect  of  Current. 

LABORATORY  EXERCISE  105. — Connect  the  terminals  (called 
the  poles)  of  your  Edison-Lalande  cell  by  a  short  piece  of 
fine  iron  or  German  silver  wire.  What  temperature  change 
takes  place  in  the  wire  ? 

Chemical  Effect  of  Current. 

LABORATORY  EXERCISE  106. — Dip  a  piece  of  filter  paper  or 
blotting  paper  into  a  solution  of  starch  to  which  some  of  a 
solution  of  potassic  iodide  has  been  added.  (A  blue  color 
in  the  starch  is  a  sign  of  free  iodine,  and  a  solution  which  is 
colored  blue  should  not  be  used.)  Connect  two  short 
copper  wires  to  the  poles  of  your  cell  and  bring  their  ends 
near  together  and  in  contact  with  the  moist  paper.  Is  there 
an  indication  of  chemical  action  ? 

Connect  the  poles  of  the  electric  machine  by  a  strip  of  the 
same  moist  paper  while  you  excite  the  machine. 

What  changes  may  accompany  the  passage  of  an  electric 
current  along  a  wire  or  through  a  solution  of  potassic  iodide  ? 

Each  of  these  properties  of  the  current  will  be  studied 
more  thoroughly  under  special  heads. 

MAGNETIC    EFFECTS    OF    THE    CURRENT 

Rotation  of  a  Magnetic  Pole  about  a  Current. 

LABORATORY  EXERCISE  107. — We  have  seen  that  a  current 
along  a  straight  wire  apparently  has  a  circular  magnetic  field 
about  it.  This  being  true,  a  free  magnetic  pole  should  move 
in  a  circle  about  a  straight  current.  This  deduction  may 
be  tested  by  the  following  experiment: 


MAGNETISM  AND  ELECTRICITY 


285 


Magnetize  strongly  a  knitting-needle  and  suspend  it  by  a 
fine  thread  tied  around  its  south-seeking  end  to  a  convenient 
support  two  or  three  feet  high.  The  needle  will  then  hang 
vertical  with  its  north-seeking  pole  downward. 

Place  an  upright  brass  or  copper  rod,  as  the  rod  of  a  ring 
stand,  or  a  large  copper  wjre  held  upright  by  means  of  a 


FIG.  78. 

convenient  clamp,  directly  below  the  point  of  attachment  of 
the  thread  to  its  support  and  so  that  its  top  will  reach  nearly 
to  the  center  of  the  suspended  needle.  The  needle  will  then 
rest  against  the  rod.  Attach  one  wire  of  the  Edison-Lalande 
cell  (or  some  other  low-resistance  cell)  to  the  lower  end  of 
the  brass  or  copper  rod,  and  taking  the  wire  from  the  other 


286  PHYSICS 

pole  of  the  battery  in  the  hand,  and  holding  the  wire  hori- 
zontal, touch  its  end  to  the  top  of  the  rod,  as  shown  in 
Fig.  78.  As  soon  as  the  current  is  set  up  in  the  rod,  the 
needle  will  start  to  rotate  around  it.  Take  the  wire  away 
from  in  front  of  the  needle  and  make  the  contact  again 
immediately  behind  the  needle  as  soon  as  it  has  passed.  By 
removing  the  wire  for  the  needle  to  pass,  and  keeping  it  upon 
the  rod  the  rest  of  the  time,  the  needle  can  be  made  to  swing 
with  accelerated  velocity  around  the  current. 

Change  the  direction  of  the  current  by  connecting  the 
other  pole  of  the  cell  to  the  bottom  of  the  rod  and  note  the 
direction  of  the  rotation  of  the  magnetic  pole  around  the 
wire.  Looking  along  the  rod  in  the  direction  of  the  current, 
is  the  rotation  of  the  magnetic  pole  clockwise  or  counter- 
clockwise.about  the  current  ? 

With  which  hand  must  you  take  hold  of  the  rod  with  the 
thumb  pointing  in  the  direction  of  the  current  so  that  the 
fingers  may  point  in  the  positive  direction  of  the  lines  of 
magnetic  force  ? 

The  Galvanometer. — The  galvanometer  is  an  instru- 
ment for  the  detection  and  measurement  of  an  electric 
current  by  means  of  its  magnetic  properties.  Galvan- 
ometers are  of  two  general  types.  In  one  a  magnetic 
needle  is  suspended  inside  a  coil  of  a  number  of  wind- 
ings of  insulated  wire.  When  a  current  passes  along 
the  wire,  the  magnetic  field  set  up  around  each  loop 
acts  upon  the  needle  to  cause  it  to  set  in  a  definite 
direction.  If  this  direction  is  not  the  same  as  the 
direction  which  the  needle  takes  in  the  earth's  field, 
then  the  direction  of  the  needle  will  indicate  the  direc- 
tion of  the  current  in  the  wire. 

In  the  other  type  of  the  galvanometer  a  coil  of 
insulated  wire  is  suspended  in  a  strong  magnetic  field, 
as  between  the  poles  of  a  strong  horseshoe  magnet. 
When  a  current  is  sent  through  the  coil  of  wire,  it  will 
tend  to  rotate  into  a  position  in  which  its  lines  of  mag- 


MAGNETISM  AND  ELECTRICITY  287 

netic  force  are  in  the  same  direction  as  those  in  the 
field  of  the  magnet. 

A  small  compass  set  in  a  hole  in  a  block  of  wood 
with  an  insulated  wire  wound  around  it  several  times 
in  the  N.S.  direction  will  serve  very  satisfactorily  for 
the  detection  of  currents. 

The  Solenoid. — We  have  already  seen  that  a  circular 
current  has  its  included  magnetic  lines  of  force  perpen- 
dicular to  the  plane  of  the  circle,  and  that  this  fact  is 
made  use  of  in  the  construction  of  the  galvanometer. 
A  coil  of  wire  so  wound  that  a  current  may  pass  con- 
tinuously around  it  from  one  end  to  the  other  is  called 
a  Helix  or  Solenoid. 

How  should  the  magnetic  lines  of  force  run  about  a 
solenoid  carrying  a  current  ? 

Magnetic  Field  of  a  Solenoid. 

LABORATORY  EXERCISE  108. — Attach  the  terminals  of  a 
voltaic  cell  to  the  ends  of  a  solenoid  which  has  been  wound 
on  a  tube  of  cardboard  or  some  other  non-magnetic  material, 
and  by  means  of  a  small  compass  or  other  magnetic  needle 
map  the  lines  of  magnetic  force  in  and  about  the  solenoid. 

In  what  respects  is  the  solenoid  analogous  to  a  bar 
magnet  ? 

In  what  respect  does  it  differ  from  a  bar  magnet  ? 

At  which  pole  of  the  solenoid  must  you  look  in  order  that 
the  current  may  go  around  it  clockwise  ? 

The  Electro- magnet,  —  We  have  seen  in  former 
experiments  that  iron  has  a  much  greater  magnetic 
permeability  than  air,  and  that  a  piece  of  iron  placed 
in  a  magnetic  field  has  more  magnetic  lines  of  force 
passing  through  it  than  formerly  existed  in  the  same 
part  of  the  field. 

Where  would  you  place  an  iron  bar  to  have  as  many 
as  possible  of  the  magnetic  lines  of  force  of  the  solenoid 
pass  lengthwise  through  it  ? 


288  PHYSICS 

Magnetization  by  Means  of  a  Solenoid. 

LABORATORY  EXERCISE  109. — Place  a  bar  of  iron  in  such  a 
position  with  reference  to  a  solenoid  as  to  make  the  largest 
possible  number  of  lines  of  magnetic  force  pass  through  it. 
Does  it  increase  the  strength  of  the  magnetic  field  of  the 
solenoid  ? 

Take  a  solenoid  provided  with  a  movable  core  of  soft  iron, 
remove  the  core  and  send  a  current  through  the  solenoid. 
Hold  the  solenoid  so  that  it  will  produce  a  slight  deflection 
of  a  magnetic  needle,  and  without  moving  it,  push  the  iron 
core  slowly  into  the  coil.  Explain  the  effect  upon  the 
magnetic  needle. 

A  solenoid  with  its  iron  core  is  called  an  Electro-magnet. 

What  explains  the  difference  in  the  strength  of  the  mag- 
netic field  of  a  solenoid  and  its  electro-magnet  ? 

What  effect  should  it  have  upon  a  bar  of  steel  to  thrust  it 
into  a  solenoid  through  which  a  current  is  passing  ? 

Perform  the  experiment  with  an  unmagnetized  knitting- 
needle,  and  explain  the  effect  upon  it. 

Can  you  reverse  the  magnetic  polarity  of  a  magnetized 
knitting-needle  by  means  of  the  solenoid  ? 

The  Electro-magnetic  Telegraph. — There  are  very 
many  important  practical  applications  of  the  electro- 
magnet. One  of  the  best  known  of  these  is  the  electro- 
magnetic telegraph.  This  is  made  in  several  different 
forms.  The  one  in  most  common  use  in  this  country 
is  the  Morse  Sounder.  In  this  instrument  a  U-shaped 
electro-magnet  is  fastened  to  a  block  and  has  a  pivoted 
bar  placed  above  it  and  between  its  poles.  A  piece  of 
soft  iron,  called  the  armature,  is  placed  across  the 
pivoted  bar  so  as  to  lie  directly  over  the  poles  of  the 
magnet.  One  end  of  the  pivoted  bar  is  held  down  by 
a  spring,  and  the  other  end  is  free  to  move  up  and  down 
between  two  stops  placed  at  a  distance  apart  a  little 
greater  than  the  width  of  the  bar. 

When  there  is  no  current  through  the  electro-mag- 
net, the  bar  is  held  against  the  upper  stop  by  the  pull 


MAGNETISM  AND  ELECTRICITY 


289 


of  the  spring  upon  its  other  end.  When  a  current  is 
sent  through  the  magnet,  the  bar  is  pulled  down  and 
strikes  the  lower  stop,  making  a  sharp  click.  When 
the  current  is  broken  it  flies  up  and  clicks  against  the 
upper  stop.  By  making  and  breaking  the  current  by 


FIG.  79- 

means  of  a  suitable  key,  the  sounder  is  made  to  click 
the  signals  of  the  Morse  alphabet. 

The  Electric  Bell. — Describe  the  construction  and 
mode  of  working  of  an  ordinary  electric  bell  and  its 
push  button. 

ELECTRO-MAGNETIC   INDUCTION 

Induction  of  Current  by  Moving  Magnet. 

LABORATORY  EXERCISE  no. — In  the  preceding  laboratory 
exercises  we  saw  that  an  electric  current  induces  a  magnetic 
field  in  its  immediate  vicinity.  We  now  wish  to  try  the 
inverse  process  and  see  if  a  magnetic  field  may  induce  an 
electric  current. 

Connect  the  ends  of  a  solenoid  by  means  of  long  wires  to 
a  galvanometer.  Place  the  solenoid  at  such  a  distance  from 
the  galvanometer  that  a  bar  magnet  moved  about  near  the 


29o  PHYSICS 

solenoid  will  not  deflect  the  galvanometer  needle.  Take  a 
strong  bar  magnet  in  the  hand  and  thrust  it  suddenly  into 
the  solenoid.  Does  it  induce  a  current  in  the  wire  of  the 
solenoid  ? 

Does  the  current  continue  after  the  magnet  has  come  to 
rest  ? 

Draw  the  magnet  suddenly  out  of  the  solenoid  and  observe 
the  galvanometer.  Is  a  current  produced  ?  If  so,  how  does 
it  differ  from  the  current  produced  when  the  magnet  was 
thrust  into  the  coil  ? 

In  which  case  is  the  current  induced  in  the  solenoid  in 
the  same  direction  as  the  current  about  an  electromagnet 
having  its  poles  in  the  position  of  those  of  the  bar  magnet  ? 

Repeat  the  experiment,  keeping  the  magnet  at  rest  and 
moving  the  solenoid  over  it.  Are  the  effects  the  same  ? 

Can  you  get  induced  currents  from  the  solenoid  when  it 
is  at  rest  with  reference  to  the  magnet  ?  (Try  moving  both 
together. ) 

State  the  law  of  the  induction  of  currents  in  a  solenoid  by 
a  moving  magnet. 

Induction  of  Current  by  the  Magnetic  Field  of 
Another  Current. 

LABORATORY  EXERCISE  1 1 1 .  — Prepare  two  solenoids  so 
that  one  can  be  placed  inside  the  other.  Connect  the 
terminals  of  the  outer  coil  to  a  galvanometer,  and  the  ter- 
minals of  the  inner  coil  to  a  voltaic  cell.  Try  to  induce 
currents  in  the  outer  coil  by  means  of  the  magnetic  field  of 
the  inner  coil.  Describe  your  method  and  results. 

Under  what  conditions  is  the  current  induced  in  the  outer 
coil  in  the  same  direction  as  the  current  of  the  inner  coil  ? 

Put  a  core  of  soft  iron  in  your  inducing  coil  and  explain 
the  change  in  its  inducing  effect. 

Connect  the  outer  coil  to  the  cell  and  the  inner  to  the 
galvanometer.  Can  you  produce  the  same  effect  as  before  ? 

Connect  the  inner  coil  to  the  cell,  the  outer  to  the  gal- 
vanometer, and  make  and  break  the  current  in  the  inner  coil. 

To  what  movement  of  the  coil  is  the  setting  up  of  the 
current  equivalent  ?  The  breaking  of  the  current  ? 

Calling  the  induced  current  direct  when  it  is  in  the  same 
direction  around  the  coil  as  the  inducing  current,  and  inverse 
when  it  is  in  the  opposite  direction,  tell  of  two  ways  in  which 


MAGNETISM  AND  ELECTRICITY          291 

an  inverse  current  may  be  induced.  Two  ways  in  which  a 
direct  current  may  be  induced. 

When  magnetic  lines  of  force  are  passed  through  a  closed 
wire  circuit,  what  takes  place  in  the  circuit  ? 

When  the  number  of  lines  of  magnetic  force  through  a 
circuit  is  increased,  is  the  current  induced  in  the  circuit  a 
direct  or  an  inverse  current  ? 

Primary  and  Secondary  Currents. — In  the  experi- 
ments in  which  a  current  flowing  through  one  solenoid 
is  made  to  induce  a  current  in  another  solenoid,  the 
coil  through  which  the  inducing  current  flows  is  called 
the  Primary  Coil,  and  the  coil  in  which  the  current  is 
induced  is  called  the  Secondary  Coil.  The  inducing 
current  is  sometimes  called  the  Primary  Current,  and 
the  induced  current  the  Secondary  Current. 

Potential  Difference  Induced  at  Terminals  of 
Secondary  Coil. — We  know  that  the  current  which  has 
been  made  to  flow  through  the  galvanometer  in  these 
experiments  indicates  that  the  two  ends  of  the  secondary 
coil  which  are  connected  to  the  galvanometer  are  at 
different  electric  potentials,  and  that  this  potential 
difference  has  been  produced  in  some  way  by  the  mag- 
netic field  of  the  primary  current.  It  has  been  found 
that  the  potential  difference  induced  in  the  two  ends 
of  a  secondary  coil  by  a  given  primary  current  is  pro- 
portional to  the  number  of  turns  of  wire  in  the  secondary 
coil.  If  the  secondary  have  the  same  number  of  turns 
as  the  primary,  and  if  it  be  placed  so  that  the  entire 
magnetic  field  of  the  primary  will  pass  through  it,  the 
potential  difference  induced  in  the  secondary  if  the 
primary  be  suddenly  broken  will  be  the  same  as  that 
of  the  primary,  which  is  due  to  the  plates  of  the  cell  to 
which  it  is  attached.  If  the  secondary  have  ten  times 
the  number  of  windings  of  the  primary,  the  potential 


292  PHYSICS 

difference  induced  at  its  ends  may  be  ten  times  the 
potential  difference  at  the  terminals  of  the  primary. 
If,  on  the  other  hand,  the  primary  have  ten  times  the 
number  of  coils  of  the  secondary,  the  potential  differ- 
ence induced  at  the  ends  of  the  secondary  will  be  only 
one  tenth  that  at  the  terminals  of  the  primary.  This 
fact  makes  it  possible  to  change  an  instantaneous 
current  of  low  potential  difference  into  one  of  high 
potential  difference,  and  vice  versa. 

The  Induction  Coil, — The  induction  coil  is  an  instru- 
ment for  changing  an  interrupted  current  of  low  poten- 
tial difference  into  one  of  high  potential  difference.  It 
consists  of  two  solenoids,  generally  placed  with  the 
secondary  outside  the  primary.  The  secondary  gen- 
erally consists  of  a  large  number  of  turns  of  wire,  and 
in  order  that  it  may  not  be  too  large  and  too  heavy, 
fine  wire  is  generally  used.  The  terminals  of  the 
secondary  are  generally  connected  to  binding  posts, 
and  the  primary  generally  has  a  core  of  soft  iron  to 
strengthen  its  magnetic  field,  and  an  automatic  device 
for  breaking  and  closing  its  circuit  with  the  voltaic 
cell.* 

•  Experiments  with  Induction  Coil. 

LABORATORY  EXERCISE  112. — Connect  a  small  induction 
coil  to  a  voltaic  cell.  Describe  by  means  of  a  diagram  the 
automatic  interrupter  of  the  coil.  When  the  primary  current 
is  being  rapidly  made  and  broken,  attach  a  wire  to  one 
terminal  of  the  secondary  and  see  whether  you  can  get  a 
spark  to  pass  from  it  to  the  other  terminal  without  bringing 
them  in  contact. 

*When  not  provided  with  an  automatic  interrupter,  one  terminal  of 
the  coil  may  be  connected  directly  to  the  cell  and  the  other  terminal  to 
a  coarse  file.  The  wire  from  the  other  terminal  of  the  cell  may  then  be 
taken  in  the  hand  and  its  end  drawn  along  the  file,  making  and  break- 
ing the  circuit  through  the  file. 


MAGNETISM  AND  ELECTRICITY 


293 


Moisten  the  fingers  and  touch  both  terminals  of  the  pri- 
mary. Of  the  secondary. 

What  other  evidence  do  you  find  that  the  potential  differ- 
ence between  the  terminals  of  the  secondary  is  greater  than 
that  between  the  terminals  of  the  primary  ? 

vS/The  Dynamo  Machine. — Most  of  the  electrical  cur- 
rents used  for  technical  purposes  are  now  derived  from 
electro-magnetic  induction  by  means  of  machines  called 
Dynamo  Machines.  The  construction  of  these  machines 
may  be  understood  from  the  accompanying  diagrams. 
In  diagram  A,  Fig.  80,  c  represents  a  closed  coil  of 


FIG.  80. 

wire  lying  between  a  pair  of  magnetic  poles  and  parallel 
to  the  lines  of  magnetic  force  of  the  magnets.  If  the 
coil  be  rotated  into  the  position  shown  in  diagram  B, 
the  number  of  lines  of  magnetic  force  passing  through 
the  coil  will  be  greatly  increased.  While  this  increase 
is  taking  place,  a  current  will  flow  around  c.  If  the 
coil  continues  to  rotate  until  it  is  again  parallel  to  the 
magnetic  lines  of  force,  the  number  of  these  lines  pass- 


294  PHYSICS 

ing  through  it  will  decrease  again  to  zero,  and  while 
this  decrease  is  taking  place  a  current  will  be  induced 
around  the  coil  in  the  opposite  direction  to  the  first 
one.  If  the  coil  be  continuously  rotated  in  the  mag- 
netic field,  a  current  will  be  induced  in  it  alternately  in 
one  direction  and  in  the  other.  Such  a  current  is 
called  an  Alternating  Current,  and  such  a  machine  is 
called  an  Alternating  Current  Dynamo. 

By  increasing  the  number  of  rotating  coils  the  in- 
tensity of  the  current  may  be  correspondingly  increased. 
These  rotating  coils  are  insulated  from  each  other,  and 
are  wound  in  many  different  ways  in  different  machines. 
The  magnet  used  in  dynamo  machines  is  an  electro- 
magnet, and  in  some  machines  the  entire  current 
generated  is  sent  around  the  magnet,  while  in  others 
the  magnet  is  separately  excited,  that  is,  is  magnetized 
by  a  current  from  another  dynamo. 

One  important  consideration  in  designing  a  dynamo 
is  to  confine  the  magnetic  field  as  much  as  possible  to 
the  region  in  which  the  coil  (called  the  Armature  Coil) 
rotates.  To  accomplish  this,  the  magnets  are  so 
shaped  as  to  make  the  air  spaces  between  them  and 
the  armature  coil  as  small  as  possible. 

The  Direct-current  Dynamo. — If  it  is  desired  to 
have  the  current  from  the  dynamo  always  in  the  same 
direction  after  leaving  the  armature,  some  form  of 
device  known  as  a  commutator  must  be  used.  One  of 
the  simplest  forms  of  commutator  is  shown  in  diagram 
in  Fig.  81.  A  split  tube  of  copper  connected  with  the 
terminals  of  the  coil  is  placed  on  an  insulating  cylinder 
which  rotates  with  the  coil.  Two  strips  of  copper  or 
carbon,  known  as  brushes,  rest  against  the  copper  and 
serve  to  carry  off  the  current.  In  the  figure  the  upper 


MAGNETISM  AND  ELECTRICITY 


295 


part  of  the  coil  is  represented  as  rotating  toward  the 
observer,  and  the  current  flows  in  the  direction  indi- 
cated by  the  arrows.  When  the  coil  has  rotated 
through  90  degrees  the  direction  of  the  current  through 
the  coil  will  change,  but  at  the  same  time  the  brushes 
which  carry  off  the  current  will  change  to  the  other 
halves  of  the  commutator  ring,  and  the  current  will 


FIG.  81. 

continue  to  pass  out  through  the  brushes  in  the  same 
direction  as  before. 

Dynamo  machines  driven  by  steam  engines  or  water 
power  now  furnish  most  of  the  electrical  currents  used 
for  practical  work.  In  all  dynamo  currents,  the  energy 
of  the  electric  current  is  derived  from  the  mechanical 
energy  used  to  run  the  generator. 

Electric  Motors. — If  an  electric  current  be  run 
through  the  armature  of  a  direct  current  dynamo,  the 


296  PHYSICS 

armature  will  revolve.  Thus  in  the  coil  shown  in  Fig1. 
81,  if  a  current  be  allowed  to  enter  through  one  of  the 
brushes  and  pass  out  through  the  other,  the  armature 
coil  will  rotate  until  its  lines  of  magnetic  force  are 
parallel  to  those  of  the  magnet.  Just  as  it  reaches  this 
position,  the  brushes  change  to  the  opposite  sides  of 
the  commutator  ring,  and  the  direction  of  the  current 
through  the  coil  is  reversed.  This  reverses  its  mag- 
netic field,  and  causes  it  to  rotate  until  its  field  is  again 
brought  into  parallelism  with  that  of  the  magnet,  at 
which  instant  it  is  again  reversed. 

If  an  alternating-current  dynamo  be  run  as  a  motor, 
it  must  be  driven  by  an  alternating  current  which  will 
reverse  its  direction  through  the  armature  at  the  proper 
time  without  the  aid  of  a  commutator. 

Most  of  the  modern  alternating-current  motors  are 
known  as  polyphase  motors,  and  are  run  by  a  current 
which  is  divided  into  two  or  more  currents  which  run 
through  different  coils  of  the  armature,  and  which 
reverse  their  direction  at  different  times,  so  that  they 
are  not  all  in  the  same  phase.  The  principle  upon 
which  these  polyphase  motors  work  has  not  been  dis- 
cussed in  these  lessons. 

The  dynamo  and  motor  combined  serve  as  a  means 
of  distributing  power  more  easily  and  economically 
than  by  any  other  method.  In  other  ordinary  methods 
of  power  distribution  the  engine  must  be  coupled  to  the 
machine  which  it  runs  by  means  of  a  shaft,  belt,  or 
cable,  so  that  the  distance  between  the  machine  and 
engine  cannot  be  great.  In  the  electrical  distribution 
of  power,  the  engine  and  dynamo  are  coupled  together, 
and  the  current  may  be  carried  over  wires  to  a  great 
distance  to  the  motor  which  drives  the  machine. 


MAGNETISM  AND  ELECTRICITY          297 

Experiments  with  the  Dynamo  Machine  and  the 
Motor. 

LABORATORY  EXERCISE  113. — Examine  and  describe  the 
parts  of  a  small  motor.  (A  toy  motor  costing  one  or  two 
dollars  is  sufficient.) 

Attach  it  to  a  cell  and  run  it  as  a  motor,  then  disconnect 
from  the  cell  and  attach  it  to  a  galvanometer  and  run  it  as  a 
dynamo. 

To  get  a  current  in  the  same  direction  through  the  arma- 
ture as  the  current  of  the  cell,  do  you  rotate  the  armature  in 
the  same  direction  that  it  was  rotated  by  the  cell,  or  in  the 
opposite  direction  ? 

The  Transformer. — In  the  distribution  of  power  by 
means  of  alternating  dynamo  currents  it  is  often 
economical  to  use  what  are  known  as  high  potential 
currents,  that  is,  currents  in  which  the  potential  differ- 


FIG.  82. 


ence  between  the  two  wires  from  the  dynamo  is  very 
great.  Such  currents  are  not  well  adapted  to  running 
motors  or  lighting  houses,  and  accordingly  some 
method  of  reducing  the  potential  difference  is  needed. 
The  instrument  by  which  this  is  accomplished  is  called 


298  PHYSICS 

a  Transformer.  In  principle,  it  is  a  reversed  induction 
coil.  One  of  its  simplest  forms  is  an  iron  ring  upon 
which  are  wound  two  coils  of  insulated  wire,  the  one 
made  of  many  turns,  and  the  other  of  only  a  few  as 
shown  in  Fig.  82.  The  alternating  current  is  run  through 
the  longer  coil,  and  at  each  reversal  it  induces  currents 
of  lower  potential  difference  in  the  shorter  coil.  These 
currents  are  then  led  to  the  motor  or  the  electric  lamp. 
The  Electro-magnetic  Telephone. 

LABORATORY  EXERCISE  114. — Another  important  instru- 
ment based  upon  the  principles  of  electromagnetic  induction 
is  the  Telephone.  One  form  of  the  telephone  may  be 
understood  from  the  following  exercise : 

Connect  the  terminals  of  a  solenoid  to  a  galvanometer, 
place  a  bar  of  soft  iron  in  the  solenoid,  and  bring  one  pole 
of  a  magnet  suddenly  near  the  end  of  the  bar.  Explain  the 
effect  upon  the  galvanometer. 

Remove  the  bar  of  soft  iron  and  insert  a  bar  magnet  into 
the  solenoid.  After  the  galvanometer  has  come  to  rest, 
bring  the  bar  of  soft  iron  suddenly  near  one  pole  of  the 
magnet.  If  your  galvanometer  is  sufficiently  sensitive,  it 
will  show  that  you  have  induced  a  current  in  the  solenoid. 
Explain  this  current. 

Induction  of  Telephone  Current. — The  so-called 
Telephone  Current  is  induced  as  follows :  A  bar  mag- 


FIG.  83. 

net,  M  in  Fig.  83,  has  a  coil  of  insulated  wire  wound 
around   one   pole,  and  a  thin  disc  of  iron,    ab  in  the 


MAGNETISM  AND  ELECTRICITY  299 

figure,  fixed  parallel  to  and  very  near  the  same  end  of 
the  magnet.  A  mouthpiece  is  fitted  just  outside  the 
iron  disc.  When  words  are  spoken  into  this  mouth- 
piece, the  sound  waves  of  the  voice  set  up  vibrations 
in  the  iron  disc  and  cause  it  to  alternately  approach 
and  recede  from  the  end  of  the  magnet.  The  vibra- 
tions of  the  disc  change  the  strength  of  the  magnetic 
field,  and  accordingly  the  number  of  magnetic  lines  of 
force  which  pass  through  the  coil,  and  thus  induce 
momentary  currents  in  opposite  directions  through  the 
coil. 

Production  of  Sound  Waves  by  Telephone. — If  an 
exactly  similar  instrument  be  placed  at  a  distance  and 
the  coils  of  the  two  instruments  be  connected,  the  cur- 
rents induced  in  one  coil  will  flow  through  the  other 
and  alternately  strengthen  and  weaken  the  field  of  its 
magnet.  This  will  cause  the  attraction  between  the 
magnet  and  its  iron  disc  to  vary,  and  will  set  up  vibra- 
tions in  the  disc  corresponding  to  the  vibrations  set  up 
by  the  voice  in  the  other  disc.  These  vibrations  of  the 
disc  will,  in  turn,  set  up  sound  waves  in  the  air  corre- 
sponding more  or  less  closely  to  the  sound  waves  of 
the  voice  at  the  other  end  of  the  line. 

The  Bell  Telephone. — This  is  the  telephone  invented 
in  i876,by  Graham  Bell,  and  known  as  the  Bell  Tele- 
phone. The  instrument  used  by  the  speaker  is  called 
the  transmitter,  and  the  one  used  by  the  hearer  is  called 
the  receiver.  The  same  instrument  is  alternately  used 
as  a  transmitter  and  as  a  receiver. 

Other  Forms  of  Telephone. — In  the  more  recent 
telephones  an  instrument  of  the  Bell  pattern  is  used  as 
a  receiver,  and  an  entirely  different  instrument,  based 
upon  the  change  of  the  electrical  conductivity  of  carbon 


300  PHYSICS 

for  a  change  of  pressure,  is  used  as  a  transmitter.  In 
this  instrument  the  telephone  current  is  not  an  induced 
current,  but  is  furnished  by  a  voltaic  cell.  This  cur- 
rent passes  from  the  vibrating  plate  of  the  mouthpiece 
through  a  disc  or  ball  of  carbon  and  through  the  coil 
around  the  magnet  of  the  receiving  telephone.  The 
vibrations  of  the  transmitter  disc  cause  a  variation  of 
the  pressure  between  it  and  the  carbon.  When  this 
pressure  is  increased  more  current  flows,  and  when  it 
is  diminished  the  current  is  weakened.  These  varia- 
tions in  current  strength  cause  the  changes  in  the  mag- 
netic field  of  the  receiver  to  which  the  vibrations  of  its 
disc  are  due. 

HEATING   EFFECT   OF    CURRENT 

Work  Done  in  Overcoming  Resistance  of  a  Conduc- 
tor.— We  have  seen  in  the  experiments  on  static 
electricity  that  some  substances  offer  a  greater  resistance 
to  the  passage  of  an  electric  charge  than  others,  and 
we  saw  in  Laboratory  Exercise  105  that  a  wire  may 
be  heated  by  the  passage  of  an  electric  current  through 
it.  This  heating  effect  is  due  to  the  resistance  of  the 
wire.  If  an  electric  charge  or  an  electric  current  is 
driven  through  a  conductor  against  a  resistance,  work 
must  be  done,  since  work  is  done  whenever  resistance 
is  overcome  through  space. 

Energy  Used  in  Heating  Conductor. — The  nature 
of  electrical  resistance  is  not  known,  since  it  is  not 
known  what  actually  passes  along  a  conductor  carry- 
ing a  current.  It  is  a  well-known  fact,  however,  that 
some  substances  require  a  much  greater  expenditure  of 
energy  to  force  a  current  through  them  than  do  others, 
and  this  energy  is  employed  in  heating  the  conductor. 


MAGNETISM  AND  ELECTRICITY  301 

Thus  all  the  work  done  in  forcing  a  current  through  a 
wire  is  changed  into  heat  in  the  wire. 

Resistance  of  Uniform  Conductor  Proportional  to 
its  Length. — If  a  current  be  driven  through  a  conductor 
of  uniform  resistance,  the  conductor  will  be  uniformly 
heated  throughout  its  length.  If  some  parts  of  the 
conductor  offer  greater  resistance  to  the  passage  of  the 
current  than  other  parts,  these  parts  are  most  heated. 
Since  a  uniform  conductor  is  heated  alike  throughout 
its  entire  length  by  the  passage  of  a  current,  it  follows 
that  the  amount  of  energy  required  to  drive  the  current 
through  the  conductor  is  proportional  to  its  length. 
Hence  the  resistance  of  a  uniform  conductor  is  propor- 
tional to  its  length. 


ELECTRICAL   UNITS  AND   MEASUREMENTS 

Practical  Units.* — Since  electrical  currents  have 
come  to  be  so  commonly  used  for  transmitting  power, 
practical  units  of  Electromotive  Force,  Current,  and 
Resistance  are  needed.  These  practical  units  are  not 
based  directly  upon  the  absolute  units  used  in  electro- 
statics, but  .their  relations  to  the  electrostatic  units  are 
known. 

The  Volt. — The  practical  unit  of  electromotive  force 
now  in  general  use  throughout  the  world  is  called  the 
Volt.  It  is  very  approximately  equal  to  the  electro- 
motive force  of  the  ordinary  Daniell's  cell,  or  gravity 
cell,  in  which  one  metal  is  zinc  in  dilute  sulphuric  acid 
or  a  solution  of  zinc  sulphate,  and  the  other  copper 
in  a  solution  of  copper  sulphate. 

The  electromotive  force  of  the  Edison-Lalande  cell 
is  approximately  .8  volt. 

*  For  technical  definition  of  units  see  appendix  A. 


302  PHYSICS 

The  Ohm. — The  practical  unit  of  resistance  is  the 
Ohm.  It  is  very  approximately  the  resistance  of  a 
column  of  mercury  one  square  millimeter  in  cross- 
section  and  1 06  centimeters  long  at  the  temperature  of 
melting  ice,  and  is  very  nearly  the  resistance  of  a 
No.  20  copper  wire  96  feet  long. 

The  Ampere. — The  Ampere  is  the  unit  of  current 
intensity.  It  is  the  current  which  is  produced  by  an 
electromotive  force  of  one  volt  in  a  conductor  having 
a  constant  resistance  of  one  ohm. 

The  Joule. — The  energy  expended  in  driving  a  cur- 
rent of  one  ampere  through  a  resistance  of  one  ohm  for 
a  period  of  one  second  is  called  a  Joule.  It  is  equiva- 
lent to  10,000,000  ergs,  or  to  .236  gram-calorie. 
Thus  a  current  of  one  ampere  through  a  resistance  of 
one  ohm  would  generate  one  gram-calorie  of  heat  in 
4.24  seconds. 

The  Watt. — The  power  (see  page  11)  unit  corre- 
sponding to  the  joule  is  the  Watt.  Thus  an  electrical 
generator  has  a  working  capacity  of  one  watt  when  it 
does  work  at  the  rate  of  one  joule  per  second,  i.e., 
when  it  sets  up  a  current  of  one  ampere  through  a 
resistance  of  one  ohm. 

The  Kilowatt. — The  Kilowatt  is  1000  watts.  The 
capacity  of  dynamo  machines  is  generally  expressed  in 
kilowatts  as  the  working  capacity  of  steam  engines  is 
expressed  in  horse-powers.  The  horse-power  is 
equivalent  to  746  watts,  nearly,  hence  to  .746  kilowatt. 

Ohm's  Law. — It  has  been  found  that  to  drive  the 
same  current  (measured  by  the  same  deflection  of  a 
magnetic  needle)  through  different  conductors  the 
electromotive  force  (see  page  268)  must  be  increased 
just  in  proportion  as  the  resistance  of  the  conductor  is 


MAGNETISM  AND  ELECTRICITY  303 

increased.  Thus  the  current  is  diminished  as  the 
resistance  is  increased,  or  is  increased  as  the  electro- 
motive force  is  increased.  Expressed  in  the  form  of 

Electromotive  Force 
an  equation,  Current  Strength  =  • —  — ^ — r— , 

or    C  =  -  —jj— .     This  law  was  first  stated  by  Dr. 
K 

George  Ohm  in  1827,  and  has  since  been  known  as 
Ohm's  Law.  Stated  in  terms  of  electrial  units,  Ohm's 

volts 

Law  becomes  amperes  =  — r — . 

ohms 

Joule's  Law. — Instead  of  measuring  the  current 
strength  by  the  deflection  of  a  magnetic  needle,  it  may 
be  measured  by  the  quantity  of  electricity  which  passes 
any  given  cross-section  of  the  conductor  in  a  unit  of 
time  as  determined  by  any  other  method.  The  quan- 
tity of  electricity  displaced  in  one  second  by  a  current 
of  one  ampere  is  called  a  Coulomb.  Thus  the  current 
in  amperes  is  equal  to  the  total  electrical  quantity  dis- 
placed measured  in  coulombs,  divided  by  the  time  of 

flow  expressed  in  seconds,  or  C  =  -- . 

From  the  discussion  on  page  267  we  know  that  the 
work  done  in  moving  an  electric  quantity  Q  in  an  elec- 
trical field  is  W=  Q(  V  —  V'}.  If  this  amount  of  work 
is  done  in  time  /,  then  the  rate  of  work,  that  is,  the 

Q(V —  V'} 
power  of  the  current,  is  P  =  ~      — .     But  since 

—  —  Cy  the  power  of  an  electric  current  is 

P-  C(V  -  V'}, 

When  C  is  expressed  in  amperes  and  ( V  •  -  V)  in 
volts,  the  power  is  expressed  in  wattsv  hence  the  work- 


3o4  PHYSICS 

ing  capacity  of  an  electric  generator  of  any  kind  may 
be  found  by  multiplying  the  number  of  amperes  it  is 
capable  of  giving  by  the  number  of  volts  potential 
difference  it  is  capable  of  maintaining  at  its  terminals 
in  the  meantime. 

In  a  given  conductor,  doubling  the  potential  differ- 
ence at  its  terminals  will  also  double  the  strength  of 
the  current  flowing  through  it ;  hence  it  will  increase 
the  power  of  the  current  fourfold.  Since  energy  is 
supplied  to  the  conductor  four  times  as  fast  as  before, 
and  since  this  energy  is  all  transformed  into  heat  in  the 
conductor,  the  heating  effect  of  the  current  will  be 
increased  fourfold  by  doubling  the  current.  Hence  the 
energy  transformed  into  heat  in  a  given  conductor 
carrying  a  current  is  proportional  to  the  square  of  the 
current. 

This  fact  was  discovered  experimentally  by  Dr. 
J.  P.  Joule  and  was  announced  by  him  in  1841,  and  it 
has  since  been  known  as  Joule's  Law. 

Since  the  heat  generated  in  a  uniform  conductor  is 
proportional  to  the  length  of  the  conductor,  it  is  pro- 
portional to  the  resistance;  hence  we  may  write 
E  —  C^Rt,  where  E  represents  the  energy  measured 
in  joules  which  is  transformed  into  heat  by  a  current 
through  a  conductor.  Expressed  in  terms  of  heat 

C^Rt 

calories,  the  equation  becomes  //=  -     — . 

4.24 

PROBLEMS. — A  current  of  3  amperes  is  maintained  through 
a  resistance  of  5  ohms.  What  is  the  potential  difference  at 
the  terminals  of  the  resistance  ? 

What  is  the  working  capacity  in  watts  of  the  battery  which 
supplies  the  current  ? 

How  many  such  batteries  would  be  required  to  furnish  a 
horse-power  ? 


MAGNETISM  AND  ELECTRICITY  305 

How  many  gram -calories  of  heat  are  generated  in  the 
resistance  in  one  minute  ? 

A  coil  of  wire  having  a  resistance  of  5  ohms  is  placed  in 
a  calorimeter  containing  500  grams  of  water  at  a  temperature 
of  10°  C.  A  current  of  2  amperes  is  run  through  the  coil 
for  ten  minutes;  neglecting  the  heat  capacity  of  the  wire  and 
the  calorimeter,  what  is  the  temperature  of  the  water  ? 

An  incandescent  lamp  having  a  resistance  of  200  ohms 
and  carrying  a  current  of  ^  ampere  is  immersed  for  ten 
minutes  in  1000  grams  of  alcohol  and  produces  a  tempera- 
ture change  of  12°.  What  is  the  specific  heat  of  alcohol  ? 

PRACTICAL  APPLICATIONS   OF   ENERGY  OF  THE 
CURRENT 

Electric  Lighting. — The  heating  effect  of  the  current 
is  made  of  great  practical  use  in  electric  lighting. 
This  is  accomplished  by  concentrating  most  of  the 
resistance  of  the  circuit  in  certain  conductors  which  are 
heated  to  incandescence  by  the  current. 

The  Incandescent  Lamp. — There  are  two  general 
forms  of  electric  lights,  known  as  the  incandescent,  or 
glow,  lamps  and  the  arc  lamps.  In  most  of  the  former 
a  conductor  of  carbon  having  a  very  high  resistance  is 
enclosed  in  a  glass  bulb  from  which  the  air  has  been 
exhausted,  so  that  the  carbon  cannot  burn,  and  is 
heated  white  hot  by  a  current  which  enters  and  leaves 
through  small  platinum  wires  sealed  into  the  glass. 
The  carbon  filament  is  made  from  a  small  strip  of 
bamboo  fiber  or  from  a  silk  or  cotton  thread  which  has 
been  carbonized  by  heating  it  red  hot  in  an  atmosphere 
of  gasoline  vapor  or  some  hydrocarbon  vapor  in  which 
it  cannot  take  fire. 

The  carbons  of  incandescent  lamps  are  adjusted  to 
a  definite  resistance  so  that  they  will  be  heated  to  the 
proper  temperature  by  a  certain  potential  difference 
(usually  from  50  to  150  volts)  maintained  at  their 


3o6  PHYSICS 

terminals.     They    are    then    connected    between    two 
wires  which  are  maintained  at  this  potential  difference. 

A  i6-candle-power  lamp  has  when  hot  a  resistance  of  200 
ohms  and  is  used  on  a  circuit  having  a  potential  difference 
of  100  volts.  What  is  the  cost  of  running  the  lamp  at  the 
rate  of  ten  cents  per  kilowatt-hour  ? 

The  Arc  Lamp. — The  arc  light  is  produced  by  the 
passage  of  a  current  between  two  carbon  points,  usually 
in  the  air.  The  current  is  first  started  with  the  carbons 
in  contact,  after  which  they  are  separated  by  hand,  or 
by  a  magnetic  device  worked  by  the  current.  When 
they  are  separated,  a  very  high  resistance  is  developed 
in  the  air  gap  between  them,  and  the  ends  of  the  car- 
bons and  the  intervening  air  are  made  very  hot.  The 
hot  air  becomes  a  conductor,  and  the  current  continues 
to  flow.  The  heat  generated  at  the  surface  of  the 
carbon  is  sufficient  to  vaporize  some  of  the  carbon,  and 
the  air  space  between  the  carbon  points  becomes  filled 
with  incandescent  carbon  vapor.  This  and  the  hot 
ends  of  the  carbons  are  the  principal  source  of  light  in 
the  electric,  or  voltaic,  arc. 

Efficiency  of  Lamps. — The  ordinary  arc  lamp  gives 
about  one  candle-power  for  each  watt,  while  an  incan- 
descent lamp  uses  three  or  four  watts  per  candle-power. 

Electric  Welding. — The  great  heat  developed  at  the 
air  space  in  the  voltaic  arc  is  often  used  to  soften  metals 
for  welding.  The  ends  of  two  metal  bars  are  brought 
together  and  the  heat  developed  by  the  high  resist- 
ance at  their  junction  is  sufficient  to  melt  the  ends  of 
the  bars.  They  are  then  forced  together  under  heavy 
pressure,  and  the  current  is  turned  off.  Iron  or  steel 
bars  as  large  as  railroad  rails  are  often  welded  in  this 
way. 


MAGNETISM  AND  ELECTRICITY  307 

The  Electric  Furnace. — The  electric  furnace  is  a 
device  for  utilizing  the  high  temperature  of  the  electric 
arc,  which  may  be  as  great  as  8000°  C.,  for  melting 
refractory  substances  and  for  producing  chemical 
changes  which  take  place  only  at  high  temperatures. 
Many  forms  of  the  electric  furnace  are  in  use,  some  of 
them  being  adapted  to  metallurgical  operations  on  a 
large  scale,  as  the  reduction  of  aluminum  from  its  ores. 

A  simple  form  of  the  electric  furnace  is  made  by 
forming  a  cavity  in  a  block  of  lime  or  fire-clay,  and 
introducing  the  carbons  through  holes  in  the  block. 
The  substance  to  be  heated  is  placed  between  and  just 
below  the  ends  of  the  carbons  which  are  directed 
downward  at  an  angle  with  each  other. 

Electric  Heating. — It  is  plain  that  the  electric  cur- 
rent may  be  used  for  heating  and  cooking  purposes, 
but  its  expense  precludes  its  use  in  this  way  except  in 
rare  cases. 

If  electric  power  costs  at  the  rate  of  ten  cents  per  kilo- 
watt-hour, what  will  be  the  cost  of  heating  four  liters  of 
water  from  20°  C.  to  the  boiling  point,  supposing  twenty 
per  cent  of  the  heat  to  be  lost  to  the  air  and  the  containing 
vessel  ? 

Loss  of  Energy  in  Electrical  Transmission.— In  all 

electrical  distribution  of  power  a  portion  of  the  energy 
is  used  in  driving  the  current  through  the  distributing 
wires  to  the  places  where  it  is  to  be  used.  Since 
the  rate  at  which  energy  is  carried  by  the  wire  is 
P  =  C(V  —  V),  it  is  possible  to  increase  this  rate  by 
increasing  either  the  potential  difference  or  the  current. 
If  the  energy  were  all  used  in  the  line  wire,  increasing 
the  potential  difference  would  increase  the  current  also; 
but  if  the  energy  is  mostly  used  in  other  conductors 


3o8  PHYSICS 

along  the  line,  as  electric  lights,  the  potential  difference 
may  be  greatly  increased  without  producing  a  corre- 
sponding increase  in  the  current.  Thus,  suppose  it  is 
desired  to  run  100  electric  lamps  of  16  candle-power 
on  a  circuit.  If  each  lamp  requires  a  power  of  50  watts 
to  sustain  it,  this  may  be  produced  in  various  ways. 
Thus  it  may  take  a  current  of  half  an  ampere  with  a 
potential  difference  of  100  volts,  or  a  current  of  one 
ampere  with  a  potential  difference  of  50  volts.  In  the 
one  case  the  line  wires  would  be  kept  at  a  potential 
difference  of  100  volts,  the  lamps  would  each  have  200 
ohms  resistance  and  would  be  connected  across  the 
wires,  and  the  wires  would  carry  50  amperes  of  current. 
In  the  other  case  the  wires  would  be  kept  at  a  poten- 
tial difference  of  50  volts,  the  lamps  would  have  a 
resistance  of  50  ohms  and  would  require  100  amperes 
of  current. 

We  have  seen  that  the  loss  of  energy  in  the  wires  is 
expressed  by  the  equation  E  =  C^Rt.  If  the  resistance 
of  the  line  wires  remains  the  same  in  the  two  cases, 
the  heating  effect  of  the  current  in  the  line  is  four  times 
as  great  in  the  second  case  as  in  the  first.  To  reduce 
this  loss  of  energy  to  that  of  the  first  case,  the  resist- 
ance of  the  line  wires  must  be  made  only  one  fourth  as 
great,  that  is,  their  carrying  power  must  be  made  four 
times  as  great,  hence  four  times  as  many  wires  of  the 
same  size  must  be  used. 

It  is  accordingly  much  more  economical  to  distribute 
the  energy  at  a  high  potential  difference,  especially 
where  it  is  to  be  carried  to  a  great  distance.  A  poten- 
tial difference  of  from  2000  to  6000  volts  is  sometimes 
used  in  arc  lights  for  lighting  streets,  but  such  potential 
differences  are  dangerous  in  houses  or  where  persons 


MAGNETISM  AND  ELECTRICITY  309 

may  come  in  contact  with  the  wires.  In  such  cases 
a  potential  difference  of  200  volts  is  as  great  as  is 
regarded  as  safe,  and  100  volts  is  considered  safer.  It 
is  for  the  purpose  of  reducing  these  high  potential 
differences  to  the  safe  lower  potential  differences  that 
transformers  are  used.  When  it  is  thought  desirable 
to  distribute  the  power  at  a  high  potential  difference, 
alternating  currents  are  used,  and  these  are  run  through 
long  transformer  coils  of  high  resistance  and  induce 
currents  of  lower  potential  difference  and  greater  cur- 
rent strength  in  the  shorter  coils  of  the  transformers. 
Thus  since  the  rate  at  which  the  energy  is  used  in 
inducing  the  new  currents  is  P=  C(V  —  V'},  if 
(V  —  Vf]  be  reduced  from  1000  to  100,  C  will  be 
increased  ten  times,  providing  there  is  no  loss  of  energy 
to  the  transformer.  There  is,  however,  always  a  loss 
of  energy  in  the  transformer,  the  iron  core  of  which 
becomes  heated. 

In  long-distance  transmission  of  power  by  electric 
currents  potential  differences  of  60,000  volts  nave  been 
successfully  used,  and  several  electric  plants  distribute 
power  at  a  potential  difference  of  40,000  volts. 

CHEMICAL   EFFECTS   OF  THE  CURRENT 

Current  Through  Solutions  Accompanied  by  Chem- 
ical Changes. — We  have  already  seen  that  the  genera- 
tion of  a  current  in  the  voltaic  cell  is  accompanied  by 
chemical  changes;  that  owing  to  a  greater  tendency 
of  one  metal  to  go  into  solution  it  discharges  positively 
charged  ions  into  the  solution,  while  the  electro-posi- 
tive ions  of  the  substance  already  in  solution  go  to  the 
other  plate  of  the  cell,  carrying  their  positive  charges 
with  them. 


3io  PHYSICS 

If  two  conducting  plates  which  do  not  go  into  solu- 
tion be  connected  to  the  terminals  of  a  battery  of 
voltaic  cells  or  a  dynamo  and  be  kept  at  a  constant 
difference  of  potential  while  in  a  solution  of  a  metallic 
salt  or  an  acid,  a  current  will  be  set  up  in  the  liquid 
by  means  of  the  ions  of  the  dissolved  substance,  the 
electro-positive  ions  going  to  one  plate  and  the  electro- 
negative ions  to  the  other. 

Conduction  of  Current  by  Copper  Sulphate  Solu- 
tion. 

LABORATORY  EXERCISE  115. — Place  two  rods  or  plates  of 
carbon  in  a  water  solution  of  copper  sulphate,  connect  them 
by  means  of  copper  wires  to  the  terminals  of  a  galvanometer, 
and  determine  whether  any  current  is  passing  through  them. 
Is  there  any  evidence  of  chemical  action  in  the  liquid  ? 

Introduce  into  the  circuit  between  the  carbons  and  the 
galvanometer  two  voltaic  cells  which  have  been  joined 
together  by  a  copper  wire  from  the  zinc  of  one  cell  to  the 
copper  or  carbon  of  the  other.  Does  a  current  now  pass 
through  the  liquid  ? 

After  the  current  has  been  established  for  a  short  time, 
withdraw  the  carbons  and  examine  them  for  indications  of 
chemical  action. 

The  electro-positive  ion  of  the  solution  travels  in  the 
direction  of  the  current.  Which  is  the  electro-positive  ion  ? 

Repeat  the  experiment,  using  strips  of  copper  foil  in  place 
of  the  carbons.  After  the  current  has  been  established  for 
some  time,  examine  both  copper  strips  for  evidence  of 
chemical  action.  What  evidence  have  you  that  the  electro- 
negative ion  goes  to  one  strip  ? 

After  one  of  the  carbons  in  your  first  experiment  has 
become  coated  with  copper,  how  would  you  change  the 
battery  connection  to  remove  the  copper  ? 

Suggest  a  method  of  electroplating  a  conductor  with 
copper.  With  silver. 

This  method  of  plating  one  metal  with  another  is  exten- 
sively used  in  the  arts. 


MAGNETISM  AND  ELECTRICITY          311 

Dissociation  of  Water  by  Current. 

LABORATORY  EXERCISE  116. — A  glass  vessel  has  two  small 
rods  of  carbon  or  strips  of  platinum  sealed  into  its  bottom 
and  connected  to  copper  wires.*  Fill  the  vessel  to  a  height 
of  about  a  centimeter  above  the  tops  of  the  carbons  with 
water  to  which  about  five  per  cent  of  sulphuric  acid  has  been 
added.  Fill  two  test  tubes  with  water  and  invert  them  in 
the  vessel  and  over  the  carbons,  raise  them  until  their  mouths 
are  just  below  the  tops  of  the  carbons,  and  fasten  them  in 
this  position. 

Attach  the  wires  to  as  many  cells  as  you  have  at  hand, 
joining  the  cells  in  line  with  the  zinc  of  one  attached  to  the 
carbon  or  copper  of  the  next  one,  and  attaching  the  free  zinc 
to  one  wire  and  the  free  copper  to  the  other. 

Observe  the  bubbles  of  gas  which  come  off  from  the 
carbons  (called  the  electrodes)  while  the  current  is  passing, 
and  arrange  the  test  tubes  so  that  all  of  this  gas  will  be  col- 
lected. After  a  sufficient  quantity  has  been  collected  for 
testing,  observe  the  volume  in  each  test  tube,  and  test  the 
larger  volume  for  hydrogen  and  the  smaller  for  oxygen. 

What  is  the  electro-positive  ion  in  the  solution  ?  The 
electro-negative  ion  ? 

The  electrode  by  which  the  current  enters  the  solution  is 


*  A  suitable  vessel  may  be  made  from  a  funnel  or  from  the  top  of  a 
bottle  which  has  been  cut  off  about  midway 
of  its  height.  Two  small  rods  of  carbon  or 
strips  of  platinum  foil  are  soldered  to  the 
ends  of  two  copper  wires.  If  the  wires  are 
to  be  soldered  to  carbon,  the  ends  of  the 
carbon  rods  should  be  heavily  plated  with 
copper  from  a  solution  of  copper  sulphate 
by  the  method  given  in  the  preceding  exer- 
cise. The  wires  should  be  passed  through 
a  cork  in  the  mouth  of  the  bottle  or  the  stem 
of  the  funnel,  taking  care  to  keep  them  sep- 
arated. The  carbons  should  be  held  in  po- 
sition about  a  centimeter  apart,  and  the 
vessel  should  be  filled  with  melted  sealing  FlG> 

wax,  pitch,  or  hard  paraffin  to  a  sufficient  height  to  cover  the  copper 
wires. 


3i2  PHYSICS 

called  the  Anode,  and  the  one  by  which  it  leaves  is  called 
the  Kathode. 

What  gas  is  set  free  at  the  anode  ?     At  the  kathode  ? 

Electrolysis. — The  method  of  current  conduction 
studied  in  the  preceding  exercises  is  known  as  Elec- 
trolysis, or  Electrolytic  Conductivity.  In  electrolysis 
the  passage  of  a  current  is  always  accompanied  by  the 
movement  of  the  dissociated  parts  of  the  dissolved 
molecules,  and  the  current  is  carried  by  these  ions. 
Thus  it  is  by  electrolysis  that  the  current  passes 
through  a  voltaic  cell. 

Theory  of  Electrolysis. — It  is  generally  believed 
that  in  any  water  solution  which  is  capable  of  electro- 
lytic conductivity  some  of  the  molecules  are  being 
constantly  broken  up  into  their  ions,  and  that  these 
ions  are  constantly  recombining  to  form  new  molecules. 
This  makes  it  necessary  that  there  should  be  in  the 
solution  at  all  times  a  number  of  free  ions,  half  of  which 
are  electro-positive  and  half  electro-negative.  When 
an  electric  field  is  established  in  the  liquid,  the  positive 
ions  move  toward  the  negative  electrode  and  the  nega- 
tive ions  toward  the  positive  electrode.  These  ions 
move  but  a  very  small  distance  before  they  recombine 
with  other  ions ;  but,  on  the  whole,  there  is  a  move- 
ment of  positive  ions  in  one  direction  through  the  liquid 
and  of  negative  ions  in  the  opposite  direction.  When 
these  ions  come  in  contact  with  the  oppositely  charged 
electrode,  they  give  their  charges  to  it,  or  take  opposite 
charges  from  it,  and  either  combine  with  the  electrode 
or  with  other  ions  of  their  own  kind  and,  if  gaseous, 
escape  from  the  solution. 

Measurement  of  Current  Strength  by  Means  of 
Electrolysis. — The    phenomenon    of  electrolysis  was 


MAGNETISM  AND  ELECTRICITY          313 

first  discovered  by  Carlisle  and  Nicholson  in  the  year 
1 800,  but  the  subject  of  electrolytic  conductivity  was 
first  fully  investigated  by  Faraday  in  1834.  Faraday 
found  that  not  the  slightest  current  can  pass  through 
an  electrolytic  solution  without  the  decomposition  of  a 
part  of  the  solution.  He  also  found  that  if  the  same 
current  was  passed  through  a  number  of  vessels  con- 
taining acidulated  water,  the  amount  of  hydrogen  and 
oxygen  set  free  was  the  same  in  each  vessel,  regardless 
of  the  size  or  shape  of  the  vessel  or  electrodes  or  of  the 
strength  of  the  solution.  If  a  current  after  passing 
through  a  vessel  of  acidulated  water  was  divided  into 
two  branches  and  passed  through  vessels  of  acidulated 
water  in  both  branches,  the  total  quantity  of  gases 
given  off  in  the  branches  was  equal  to  the  quantity 
given  off  in  the  main  current. 

These  experiments  showed  Faraday  that  the  amount 
of  decomposition  in  the  circuit  was  proportional  to  the 
current,  and  accordingly  that  the  quantity  of  gases 
given  off  in  a  second  might  be  taken  as  the  measure  of 
the  current  strength. 

The  Voltameter.  —  An  instrument  arranged  for 
measuring  the  strength  of  a  current  by  the  amount  of 
chemical  decomposition  which  it  produces  is  called  a 
Voltameter.  The  apparatus  used  in  Exercise  115  or 
1 1 6  may  be  used  as  a  voltameter  by  weighing  the 
copper  deposited  or  by  measuring  the  gases  given  off. 
The  voltameter  method  of  measuring  a  current  is  so 
accurate  that  the  ampere  has  been  defined  by  the 
amount  of  silver  which  it  will  deposit  in  one  second  in 
a  properly  constructed  silver  voltameter.  The  copper 
voltameter  is  also  largely  used,  especially  in  technical 
work. 


314  PHYSICS 

Faraday  also  found  that  if  the  same  current  was 
passed  through  a  number  of  voltameters  containing 
different  solutions,  the  amount  of  decomposition  in  one 
was  chemically  equivalent  to  the  amount  of  decomposi- 
tion in  another.  Thus  one  gram  of  hydrogen  is 
replaced  in  a  chemical  compound  by  108  grams  of  silver 
or  31.6  grams  of  copper.  If  a  water  voltameter,  a 
voltameter  containing  a  solution  of  silver  nitrate  and 
one  containing  a  solution  of  copper  sulphate  be  con- 
nected in  a  line  and  the  same  current  be  sent  through 
them  all,  when  one  gram  of  hydrogen  has  been  set  free 
in  the  water  voltameter,  108  grams  of  silver  and  31.6 
grams  of  copper  will  have  been  deposited  in  their 
respective  voltameters. 

Electro- chemical  Equivalents. — The  electro-chem- 
ical equivalent  of  a  substance  is  the  amount  by  weight 
of  the  substance  which  will  be  set  free  from  a  solution 
in  one  second  by  a  current  of  one  ampere,  that  is,  by 
one  coulomb  of  electricity.  The  electro-chemical 
equivalents  of  the  elements  bear  the  same  ratios  as  the 
combining  weights  of  the  elements  when  they  form 
chemical  compounds. 

The  electro-chemical  equivalent  of  hydrogen  is  .00001038 
gram.  What  is  the  electro-chemical  equivalent  of  silver  ? 
Of  copper  ? 

Electrolytic  Polarization.  —  It  has  already  been 
mentioned  that  when  the  products  of  electrolytic  dis- 
sociation are  deposited  upon  the  plates  of  a  voltaic  cell 
they  may  decrease  the  electromotive  force  of  the  cell. 
Thus  the  potential  difference  between  zinc  and  hydrogen 
is  less  than  between  zinc  and  carbon,  hence  the  current 
of  a  cell  made  of  zinc  and  carbon  is  greatly  decreased 
when  the  carbon  plate  becomes  coated  with  hydrogen. 


MAGNETISM  AND  ELECTRICITY  31 5 

The  same  thing  is  true  of  zinc  and  carbon  in  a  copper 
sulphate  solution.  The  potential  difference  between 
zinc  and  copper  is  less  than  between  zinc  and  carbon, 
hence  the  electromotive  force  of  the  cell  is  weakened 
when  the  carbon  plate  becomes  coated  with  copper. 

When  a  cell  is  weakened  by  the  deposition  of  the 
products  of  electrolysis  upon  one  or  both  of  its  plates, 
the  cell  is  said  to  be  polarized.  The  two  similar  plates 
in  the  voltameter  may  likewise  be  said  to  be  polarized 
by  the  changes  which  take  place  on  their  surface  during 
the  passage  of  a  current. 

Currents  due  to  Polarization. 

LABORATORY  EXERCISE  117.  — Attach  copper  wires  to  two 
strips  of  sheet  lead  of  convenient  size,  stand  them  in  a 
tumbler  of  dilute  sulphuric  acid  solution  at  a  distance  of 
about  a  centimeter  from  each  other,  and  connect  them  to  a 
galvanometer.  Do  they  form  a  voltaic  cell  ? 

Send  a  current  through  them  from  two  or  more  cells 
arranged  as  for  the  water  voltameter.  Notice  carefully  the 
direction  of  the  current  through  the  liquid.  After  the  cur- 
rent has  passed  for  several  minutes,  disconnect  the  battery 
and  connect  the  plates  again  to  the  galvanometer  and  note 
the  direction  of  the  current.  Allow  the  current  to  flow  for 
some  time.  Does  the  cell  finally  run  down  ? 

Storage  Cells. — The  lead  plates  in  the  sulphuric  acid 
solution  form  what  is  called  a  Storage  Cell  or  Accumu- 
lator, though  it  does  not  in  reality  store  up  electricity. 
The  lead  of  one  plate  is  acted  upon  by  the  oxygen  of 
the  current,  and  that  of  the  other  plate  by  the  hydrogen. 
The  one  accordingly  becomes  coated  with  lead  oxide, 
while  the  oxide  already  formed  on  the  surface  of  the 
other  is  removed  by  the  hydrogen,  leaving  a  clean  lead 
surface.  When  the  current  is  broken,  the  lead  is  more 
strongly  electro-positive  than  the  lead  oxide,  and  it 
accordingly  combines  with  the  electro-negative  ion  of 


316  PHYSICS 

the  solution  and  becomes  oxidized,  while  the  hydrogen, 
the  electro-positive  ion  of  the  solution,  goes  to  the  lead 
oxide  plate  and  reduces  the  oxide  to  metallic  lead. 
When  the  two  plates  reach  the  same  stage  of  oxidation, 
the  potential  difference  between  them  disappears,  and 
the  current  ceases. 

The  first  storage  cells  were  made  of  lead  plates  as  in 
the  preceding  experiment,  but  most  storage  cells  are 
now  made  by  filling  a  porous  lead  plate,  called  a  grid, 
with  a  paste  made  of  red  lead,  a  lead  oxide.  This 
paste  is  reduced  to  metallic  lead  in  one  plate,  and  is 
still  further  oxidized  in  the  other  by  the  passage  of  the 
current. 

Some  of  the  ordinary  voltaic  cells  may  be  used  as 
storage  cells.  For  example,  the  plates  of  the  Edison- 
Lalande  cell  are  composed  of  zinc  and  copper  oxide. 
The  hydrogen  goes  to  the  copper  oxide  plate  and 
reduces  it  to  metallic  copper,  after  which  the  cell 
becomes  useless.  By  sending  a  current  through  the 
cell  in  the  opposite  direction  the  copper  plates  could 
be  again  oxidized,  but  the  zinc  plate  could  not  be 
restored  to  its  former  efficiency  in  this  way. 

Internal  Resistance  of  Cells. — We  have  found  in 
our  experiments  on  electrolysis  that  an  electrolytic 
solution  offers  a  considerable  resistance  to  the  passage 
of  a  current,  so  that  several  cells  are  necessary  to 
maintain  a  strong  current  through  such  a  solution. 
The  same  thing  is  true  of  the  electrolytic  liquid  in  a 
voltaic  cell.  If  the  two  plates  of  the  cell  are  connected 
by  a  short  copper  wire  or  a  conductor  of  any  kind 
having  a  low  resistance,  they  are  said  to  be  short-cir- 
cuited. In  this  condition  the  principal  resistance  to 
the  passage  of  a  current  is  found  to  be  in  the  liquid  of 


MAGNETISM  AND  ELECTRICITY  317 

the  cell.  This  resistance  seems  to  be  principally  due 
to  the  resistance  which  the  ions  meet  with  in  their 
passage  through  the  liquid,  and  all  the  energy  expended 
in  driving  the  current  through  the  liquid  is  transformed 
into  heat. 

The  current  which  a  cell  will  give  on  short  circuit 
accordingly  depends  upon  the  electromotive  force  and 
the  internal  resistance  of  the  cell.  With  the  same 
metals  in  a  given  solution,  the  electromotive  force  of 
the  cell  cannot  be  increased,  since  the  potential  differ- 
ence between  large  pieces  of  zinc  and  copper  is  the 
same  as  between  small  pieces.  By  increasing  the  size 
of  the  plates  we  may,  however,  increase  the  current 
strength,  since  we  increase  the  number  of  ions  which 
are  carrying  charges  through  the  liquid,  and  as  this 
increases  the  current  strength  without  increasing  the 
electromotive  force,  it  is  equivalent  to  decreasing  R  in 

E.M.F. 

the  equation  C  =  — „ — . 

By  moving  the  plates  of  the  cell  closer  together 
we  may  also  decrease  the  internal  resistance  of  the 
cell. 

The  current  which  may  be  derived  from  a  cell 
through  an  external  resistance,  as  a  long  wire,  is  found 
by  dividing  the  electromotive  force  of  the  cell  by  its 
internal  resistance  plus  the  resistance  of  the  external 
conductor.  Hence  a  cell  of  low  electromotive  force 
and  low  internal  resistance,  while  it  may  give  a  strong 
current  when  short-circuited,  cannot  give  a  strong  cur- 
rent through  great  external  resistance.  An  Edison- 
Lalande  cell  of  .8  volt  E.M.F.  and  .04  ohm  internal 
resistance  may  give  on  short  circuit  a  current  of  20 
amperes,  while  a  Daniell's  cell  of  I  volt  E.M.F.  and 


3i8  PHYSICS 

3  ohms  internal  resistance  can  give  only  J  ampere  on 
short  circuit.  Through  an  external  resistance  of  20 
ohms  the  two  cells  will  give  currents  of  ^  ampere  and 
-gJj  ampere  respectively. 

Grouping  of  Cells. — We  learned  in  static  electricity 
that  metallic  conductors  when  in  contact  with  each 
other  necessarily  take  the  same  potential ;  consequently 
when  the  zinc  of  one  cell  and  the  copper  of  another  are 
connected  by  a  wire  there  can  be  no  potential  difference 
between  them.  Since  each  plate  is  maintained  at  a 
different  potential  from  the  other  plate  in  its  own  cell 
by  the  intervening  liquid,  the  potential  difference  of  the 
free  zinc  and  the  free  copper  of  the  two  cells  is  twice 
that  of  the  zinc  and  copper  of  a  single  cell.  By  con- 
necting a  number  of  cells  in  line  in  this  way,  we 
accordingly  get  a  potential  difference  at  the  terminals 
which  is  the  sum  of  the  potential  differences  of  all  the 
cells  in  the  line.  Cells  connected  in  this  way  are  said 
to  be  joined  in  series. 

Since  the  current  given  by  the  cells  when  joined  in 
series  must  flow  through  all  the  cells,  the  resistance  of 
the  line  of  cells  is  likewise  the  sum  of  the  resistances  of 
the  single  cells.  Accordingly  a  number  of  cells  joined 
in  series  will  give  the  same  current  on  short  circuit  as 
a  single  cell.  For  example,  four  Daniell's  cells  with 
an  E.M.F.  of  one  volt  and  an  internal  resistance  of 
three  ohms  will  give  when  joined  in  series  an  E.M.F. 
of  four  volts  and  an  internal  resistance  of  twelve  ohms, 
hence  a  current  of  one  third  ampere,  the  same  current 
that  a  single  cell  would  give.  If  the  external  resist- 
ance be  great,  however,  then  the  four  cells  will  give 
approximately  four  times  the  current  of  a  single  cell . 
Thus  with  an  external  resistance  of  100  ohms,  a  single 


MAGNETISM  AND  ELECTRICITY  319 

cell  will  give  a  current  C  =  T-J-g-,  while  the  four  cells 
will  give  a  current  C  =  Tf^. 

Another  method  of  connecting  the  cells  is  to  join  all 
the  zincs  to  one  wire  and  all  the  coppers  to  the  other. 
In  this  case  the  E.M.F.  is  not  increased,  since  the 
plates  which  are  joined  were  all  at  the  same  potential 
before  they  were  connected.  The  current  on  short 
circuit  is  increased,  however,  as  each  cell  gives  the 
same  current  through  the  connecting  wire  that  it  would 
give  if  it  were  not  joined  to  the  others.  This  method 
of  joining  the  cells  is  accordingly  equivalent  to  decreas- 
ing the  internal  resistance  of  the  circuit.  The  four 
Daniell's  cells  previously  considered  would  when  joined 
in  this  way  each  give  its  original  current  of  one  third 
ampere,  and  the  four  together  would  give  a  current  of 
four  thirds  ampere.  Since  this  increase  of  current  is 
accomplished  without  increasing  the  potential  differ- 
ence, it  must  be  due  to  the  decrease  of  internal  resist- 
ance. The  resistance  of  the  four  cells  joined  in  this 
way  is  accordingly  taken  as  three  fourths  an  ohm. 

Cells  connected  in  this  way  are  said  to  be  joined 
parallel. 

PROBLEMS. — What  current  would  the  four  Daniell's  cells 
joined  parallel  give  through  an  external  resistance  of  100 
ohms  ?  What  current  would  a  single  cell  give  through  the 
same  resistance  ? 

How  would  you  connect  six  Daniell's  cells  having  an 
electromotive  force  of  one  volt  and  an  internal  resistance  of 
three  ohms  so  as  to  give  a  current  of  two  amperes  on  short 
circuit  ?  (The  cells  may  be  connected  in  series  or  parallel, 
or  in  groups  of  two  or  three  parallel. ) 

How  would  you  connect  the  same  cells  to  give  the 
greatest  possible  current  through  20  ohms  external  resist- 
ance ? 


320  PHYSICS 

ELECTRIC    RADIATION 

ELECTRIC  WAVES 

Maxwell's  Theory. — In  our  discussion  of  the  pres- 
sure exerted  by  one  charge  of  static  electricity  upon 
another  through  the  intervening  Ether,  we  saw  that 
this  pressure  is  analogous  to  that  caused  by  a  displace- 
ment in  an  elastic  body,  so  that  Maxwell  named  the 
property  of  the  Ether  by  virtue  of  which  the  pressure 
is  exerted  the  Electric  Elasticity  of  the  Ether.  We 
also  learned  that  when  a  spark  discharge  takes  place 
between  a  positively  and  a  negatively  electrified  body 
the  intervening  dielectric  seems  to  give  way  to  the 
electric  pressure  and  allow  a  quantity  of  electricity  to 
pass  through.  We  also  learned  that  the  spark  dis- 
charge is  of  an  oscillatory  character,  so  that  apparently 
a  quantity  of  electricity  passes  back  and  forth  from  one 
conductor  to  the  other  several  times  before  it  finally 
comes  to  rest. 

Maxwell  argued  that  if  the  electric  pressure  were, 
as  he  supposed,  exerted  by  the  elasticity  of  the  Lumi- 
niferous  Ether,  such  an  oscillation  taking  place  in  it 
would  set  up  waves  which  would  be  transmitted  in  all 
directions,  like  sound  waves  in  air,  and  that  these 
waves  would  travel  with  the  velocity  of  light,  since 
light  travels  by  means  of  waves  in  the  same  medium. 
He  showed  that  the  time  required  for  a  spark  discharge 
to  take  place  was  greater  when  a  large  quantity  of 
electricity  was  discharged  than  when  the  quantity  was 
small,  and  accordingly  that  the  oscillations  of  the  dis- 
charge would  be  slower  the  greater  the  capacity  of  the 
discharging  conductor.  He  calculated  the  dimensions 
of  conductors  which  would  discharge  with  sufficient 


MAGNETISM  AND  ELECTRICITY  321 

rapidity  to  set  up  oscillations  as  rapid  as  those  of  light, 
and  found  that  such  conductors  would  be  of  about  the 
size  of  the  atoms  or  molecules  of  material  bodies. 
He  accordingly  advanced  the  theory  in  1 876  that  light 
waves  are  due  to  the  oscillations  set  up  by  electric  dis- 
charges or  disturbances  between  the  atoms  of  luminous 
bodies.  This  was  known  as  Maxwell's  Electromag- 
netic Theory  of  Light.  ^^cX 

Hertzian  Waves. — The  waves  set  up  in  the  Erher 
by  electric  discharges  were  experimentally  discovered 
ten  years  later  by  Prof.  Hertz,  in  Germany,  and  have 
since  been  called  the  Hertzian  Waves.  These  waves 
have  been  much  studied  and  their  properties  are  well 
known.  They  are  now  coming  into  extensive  use  in 
4 '  Wireless  Telegraphy. ' ' 

Electric  Resonance.* 

LABORATORY  EXERCISE  118. — Two  similar  Leyden  jars  of 
the  same  capacity  are  set  upon  wooden  blocks  provided  with 
upright  standards.  One  jar,  as  in  Fig.  85, 
has  a  strip  of  tin-foil  about  a  centimeter  wide 
pasted  to  the  outside  of  the  jar  and  reaching 
from  the  outer  coating  over  the  edge  of  the  jar 
and  making  connection  with  the  knob  and  the 
inner  coating.  This  strip  is  cut  down  in  one 
place  to  a  width  of  three  or  four  millimeters, 
and  after  it  has  dried  a  scratch  is  made  across 
it  with  the  point  of  a  needle,  taking  care  that 
the  contact  is  broken,  but  leaving  the  edges 
as  close  together  as  possible. 

Two  pieces  of  copper  wire  about  five  feet 
long  are  cut  of  equal  length,  and  are  passed 
through  holes  in  the  tops  and  bottoms  of  the  FIG. 
wooden  standards  and  are  bent  into  similar  loops,  as  shown 
in  Fig.  86.  One  of  these  loops  ends  in  a  small  knob,  as 
shown  in  the  figure,  while  the  corresponding  end  of  the  other 

*  The  following  experiments  may  be  used  as  laboratory  exercises,  or 
they  may  very  properly  be  performed  by  the  teacher  before  the  class. 


322 


PHYSICS 


is  attached  to  the  knob  of  the  Leyden  jar  upon  which  the  tin- 
foil strip  was  pasted.  The  other  ends  of  the  wires  are  placed 
under  the  jars,  making  contact  with  their  outer  coatings. 

Adjust  the  wire  loops  as  nearly  as  possible  alike,  and  stand 
the  two  jars  side  by  side  about  a  foot  apart  with  their  wire 
loops  parallel.  Connect  the  discharging  knobs  of  the  elec- 
tric machine  by  fine  wires  to  the  jar  without  the  tin-foil  strip, 
joining  one  wire  to  the  knob  of  the  jar  and  the  other  to  the 
small  knob  on  the  end  of  the  wire  loop.  Separate  this  knob 
a  few  millimeters  from  the  knob  of  the  jar  and  turn  the 
machine  until  the  jar  discharges  by  a  spark  between  the  two 


FIG.  86. 

knobs.  If  the  wires  on  the  two  jars  are  properly  adjusted, 
a  spark  will  pass  across  the  scratch  in  the  tin-foil  of  the  other 
jar.  If  the  spark  does  not  appear  at  once,  change  the  length 
of  one  wire  slightly  by  pushing  its  end  farther  under  the  jar, 
or  by  pulling  it  out  a  little.  This  end  should  always  make 
a  good  contact  with  the  outer  coating  of  the  jar.  With  a 
little  adjustment,  the  uncharged  jar  can  be  made  to  spark  at 
every  discharge  of  the  other  jar. 

The  two  jars,  like  the  two  resonance  forks  used  in  the 
sound  experiments,  are  tuned  to  the  same  period  of  oscilla- 
tion, but  while  the  vibration  in  the  tuning  fork  is  induced 
by  air  waves,  the  electric  vibrations  in  the  Leyden  jar  are 
induced  by  Ether  waves.  Since  the  oscillations  set  up  in 


MAGNETISM  AND   ELECTRICITY 


323 


one  jar  by  the  spark  discharge  are  of  the  same  period  as 
those  which  would  be  set  up  in  the  other  jar  by  a  similar 
discharge,  the  Ether  vibrations  induce  sympathetic  vibrations 
in  the  other  jar.  This  phenomenon  is  accordingly  known 
as  Electric  Resonance. 

Keeping  the  jars  at  the  same  distance  from  each  other, 
turn  one  of  them  until  the  plane  of  its  loop  is  at  right  angles 
to  that  of  the  other  jar.  In  this  position  you  will  be  unable 
to  get  the  uncharged  jar  to  spark. 

If  the  Ether  waves  were  compressional  waves,  the  jar 
should  spark  as  well  in  the  second  position  as  in  the  first; 
hence  they  are  apparently  waves  of  transverse  vibration  and 
cannot  set  up  oscillations  at  right  angles  to  their  own  vibra- 
tions. 

The  Coherer. 

LABORATORY  EXERCISE  119. — Take  a  glass  tube  of  about 
a  centimeter  bore  and  six  or  eight  centimeters  long,  fit  the 
ends  with  corks  through 
which  copper  wires  can  be 
passed,  and  fill  the  tube 
between  the  corks  with  brass 
or  iron  filings.  Thrust  copper 
wires  through  the  corks  and 
into  the  iron  filings  until 
their  ends  are  one  or  two 
centimeters  apart.  Connect 
these  wires  in  circuit  with 
one  or  more  voltaic  cells  and 
a  tolerably  sensitive  galvan- 
ometer. The  resistance  of 
the  filings  to  the  passage  of 
a  current  should  be  so  great 
that  the  galvanometer  is 
slightly,  if  at  all,  deflected. 

Bring  an  electric  machine 
near,  and  pass  sparks  from 
one  discharging  knob  into 
one  of  the  wires  which  enters 
the  tube.  The  resistance 
should  fall  so  that  the  gal- 
vanometer is  deflected  through  nearly  90 


FIG.  87. 


324  PHYSICS 

This  instrument  is  called  a  Coherer.  The  passage  of  the 
electric  discharge  into  the  small  metallic  particles  in  the  tube 
apparently  causes  them  to  cling  together  so  that  they  make 
better  electric  contact  than  before. 

After  your  coherer  has  become  sensitive  enough  to  allow 
the  passage  of  a  suitable  current,  increase  its  resistance  again 
by  tapping  gently  on  the  glass  and  causing  the  particles  to 
separate.  Then  move  the  electric  machine  to  a  distance  of 
a  few  feet  from  the  coherer  and  turn  the  handle  and  cause 
sparks  to  pass  between  the  discharging  knobs  of  the  machine. 
If  your  coherer  has  been  properly  adjusted,  the  galvanometer 
will  be  deflected  again,  showing  that  the  resistance  of  the 
coherer  has  been  again  diminished.  By  a  little  care  in  the 
adjustment,  and  by  using  a  sensitive  galvanometer,  the 
coherer  will  respond  to  a  spark  at  a  distance  of  several  yards. 

If  convenient,  work  the  electric  machine  on  the  opposite 
side  of  a  stone  or  wooden  wall  and  observe  that  the  electric 
waves  pass  readily  through  the  wall. 

Wireless  Telegraphy.  -  -  The  coherer  described 
above  is  similar  to  the  receiver  used  in  "  wireless 
telegraphy."  The  coherer  is  connected  between  a 
battery  and  a  telegraph  sounder,  and  is  attached  to  a 
long  wire  or  other  conductor  suspended  at  some  height. 
A  similar  conductor  is  suspended  at  the  sending  station, 
and  is  connected  with  the  spark  gap  of  the  electric 
machine  or  induction  coil.  The  oscillations  in  the 
receiving  conductor  are  accordingly  partly  due  to 
resonance,  and  they  are  sufficient  to  lower  the  resist- 
ance of  the  coherer  so  that  a  signal  can  be  made 
through  it.  An  automatic  tapper  jars  the  particles 
apart,  so  that  the  signal  is  momentary  unless  the 
instrument  is  sensitized  by  another  spark. 

ROENTGEN   RADIATION 

Electric  Discharge  in  Rarefied  Gases. — We  have 
seen  that  gases  at  atmospheric  pressure  offer  a  very 


MAGNETISM  AND  ELECTRICITY  325 

high  resistance  to  the  passage  of  the  electric  discharge. 
This  is  not  true  of  rarefied  gases.  When  the  air  is 
exhausted  from  a  glass  tube  until  it  will  sustain  a  pres- 
sure of  only  two  or  three  millimeters  of  mercury  an 
electric  discharge  may  be  readily  passed  .between  two 
metallic  electrodes  sealed  into  the  glass.  When  this 
occurs,  the  discharge  does  not  pass  as  a  spark,  but  the 
whole  interior  of  the  tube  is  lighted  up  by  a  glow. 
Tubes  prepared  in  this  way  are  called  Geissler's  Tubes. 
Kathode  Rays.— When  the  tube  is  more  highly 
exhausted  the  glow  disappears,  and  at  a  sufficiently 
high  exhaustion  a  bluish  light  is  seen  to  go  out  in 


FIG. 

straight  lines  from  the  negative  electrode,  called  the 
Kathode.  This  bluish  light  is  called  the  Kathode 
Radiation.  It  is  probably  due  in  large  part  to  electri- 
fied particles  thrown  off  from  the  kathode  by  the  dis- 
charge. Fig.  88  shows  a  tube  prepared  for  Roentgen 
Radiation  in  which  the  kathode  is  made  concave  in 
order  to  focus  the  kathode  radiation  upon  a  platinum 
plate  mounted  in  the  tube. 

Formation   of   Roentgen    Radiation. — Where    the 
kathode  radiation  strikes  upon  the  walls  of  the  tube  or 


326  PHYSICS 

upon  metal  plates  within  the  tube,  a  form  of  invisible 
radiation  is  produced  which  was  discovered  by  Professor 
Roentgen  in  1895  and  was  named  by  him  the  X-Radia- 
tion,  because  its  character  was  unknown.  It  is  now 
generally  called  the  Roentgen  Radiation,  after  its  dis- 
coverer. 

Properties  of  Roentgen  Radiation. — The  Roentgen 
Radiation,  like  the  Hertzian  Waves,  passes  readily 
through  many  substances  which  are  opaque  to  light. 
Since  it  cannot  be  seen,  it  can  only  be  detected  by  its 
electrical  or  chemical  effects.  It  is  generally  detected 
by  its  power  of  inducing  a  glow,  called  fluorescence, 
in  many  chemical  substances,  or  by  its  effect  upon  a 
photographic  plate. 

If  the  Roentgen  Radiation  is  allowed  to  fall  upon  a 
fluorescent  screen  prepared  by  coating  a  piece  of  card- 
board with  some  fluorescent  substance,  it  will  cause  the 
surfaces  of  the  screen  to  glow  with  a  faint  light,  which 
can  be  plainly  distinguished  in  a  dark  room.  A  sub- 
stance opaque  to  the  radiation,  if  held  between  the 
screen  and  the  source  of  radiation,  will  cast  a  shadow 
upon  the  screen,  just  as  an  opaque  body  held  between 
a  lighted  lamp  and  the  wall  will  cast  a  shadow  upon 
the  wall.  These  shadows  may  be  observed  directly 
upon  the  screen,  or  they  may  be  photographed  upon  a 
sensitized  plate. 

Since  the  skin  and  flesh  of  the  body  are  fairly  trans- 
parent to  Roentgen  Radiation,  the  shadows  of  the 
bones  and  of  opaque  objects  imbedded  in  the  flesh  can 
be  observed  on  the  fluorescent  screen,  hence  the  use  of 
this  form  of  radiation  in  surgery. 

Fig.  89*  is  a  photograph  taken  of  an  actual  surgical 

*  Photographed  by  Dr.  Philip  Mills  Jones,  of  San  Francisco. 


MAGNETISM  AND  ELECTRICITY 


327 


case.  It  shows  the  shadows  of  the  bones  of  a  hand  in 
which  two  of  the  metacarpal  bones  are  broken,  and 
was  taken  through  a  wooden  splint  and  bandages. 


FIG.  89. 

PROBLEMS. — What  weight  of  silver  may  be  deposited  from 
a  silver  nitrate  solution  in  ten  minutes  by  a  current  of 
5  amperes  ? 


328  PHYSICS 

What  is  the  strength  of  a  current  which  will  deposit  5.9 
grams  of  copper  in  one  hour  ? 

One  liter  of  hydrogen  weighs  89.6  milligrams;  what  is  the 
strength  of  a  current  which  will  set  free  one  cubic  centimeter 
of  hydrogen  per  minute  ? 

Five  storage  cells  each  having  an  electromotive  force  of 
2  volts  and  an  internal  resistance  of  .  i  ohm  are  joined  in 
series  with  a  copper  voltameter  and  cause  a  deposition  of 
.00984  grams  of  copper  per  minute.  What  is  the  resistance 
of  the  voltameter  ? 

What  is  the  current  strength  of  four  cells  joined  in  series, 
each  having  an  electromotive  force  of  2  volts  and  an  internal 
resistance  of  -J-  ohm — 

(a)  When  the  external  resistance  is  negligible  ? 

(b)  When  the  external  resistance  is  10  ohms  ? 

(c)  When  the  external  resistance  is  100  ohms  ? 
Calculate  the  current  given  by  the  same  cells  through  the 

same  resistances  when  the  cells  are  joined  parallel. 

A  coil  of  wire  having  a  resistance  of  100  ohms  is  immersed 
in  one  liter  of  water  at  20°  C.,  and  has  a  current  of  one 
ampere  maintained  in  it.  What  will  be  the  temperature  of 
the  water  at  the  end  of  20  minutes  ? 

An  arc  light  having  a  potential  difference  of  100  volts 
between  its  carbons  is  run  by  a  current  of  5  amperes.  What 
horse-power  does  it  absorb  ? 

What  is  the  candle-power  of  this  arc,  counting  one  watt 
per  candle-power  ? 

What  is  the  cost  of  maintaining  this  light  at  5  cents  per 
kilowatt  hour  ? 

The  resistance  of  a  copper  conductor  of  one  square  centi- 
meter cross-section  reaching  from  Niagara  to  New  York 
would  be  about  80  ohms.  What  potential  difference  must 
be  maintained  at  the  terminals  of  this  conductor  in  order  for 
it  to  carry  a  current  of  500  amperes  ? 

What  would  be  the  loss  of  energy  in  the  wire,  measured 
in  kilowatts  ? 

What  measured  in  horse-power  ? 

A  current  of  500  amperes  is  transformed  from  a  potential 
difference  of  40,000  volts  to  one  of  100  volts;  neglecting 
the  loss  of  energy  in  the  transformer,  how  many  amperes  will 
it  give  ? 


PART  VI 
OPTICS   AND   RADIATION 

DEFINITIONS 

Origin  of  Radiant  Energy. — We  have  already  seen 
that  both  heat  and  electrical  energy  may  be  transformed 
into  radiant  energy  and  transmitted  by  the  Luminiferous 
Ether. 

Light. — That  form  of  radiant  energy  which  is  the 
physical  cause  of  our  sensation  of  sight  is  called  Light. 

Optics. — That  branch  of  Physics  which  treats  of  the 
subject  of  Light  is  called  Optics. 

Radiation  Best  Studied  in  Optics. — Since  we  have 
a  special  sense  organ  which  enables  us  to  recognize 
light,  the  laws  of  radiation  may  be  more  easily  under- 
stood from  the  study  of  Optics  than  from  any  other 
branch  of  Physics. 

ORIGIN   OF   LIGHT 

Luminous  Bodies. — So  far  as  we  know,  light  always 
has  its  source  in  some  material  body.  A  body  in  which 
light  originates  is  called  a  Luminous  Body. 

PROPAGATION  OF   LIGHT 

Transmission  by  Optical  Medium. — It  is  a  familiar 
observation  that  light  travels  in  all  directions  from  the 
luminous  body  which  is  its  source.  We  also  know  that 

329 


330  PHYSICS 

it  travels  readily  through  a  vacuum,  as  otherwise  bodies 
in  a  vacuum,  as  the  filament  in  an  incandescent  lamp 
bulb,  would  be  invisible,  and  light  could  not  reach  us 
from  the  stars.  It  likewise  travels  readily  through 
many  material  bodies. 

A  substance  through  which  light  can  be  transmitted 
is  often  called  an  Optical  Medium,  or  simply  a  Medium. 
If  the  medium  allows  light  to  pass  so  readily  that 
objects  may  be  seen  through  it,  it  is  said  to  be  Trans- 
parent. If  some  light  passes  through  it,  but  not 
enough  for  distinct  vision,  the  medium  is  said  to  be 
Translucent.  Substances  which  do  not  allow  the 
passage  of  light  through  them  are  said  to  be  Opaque. 

Velocity  of  Light  Propagation. — The  velocity  of 
light  propagation  through  the  Luminiferous  Ether  of 
the  Solar  System  was  first  measured  by  Roemer,  a 
Danish  astronomer,  at  the  Paris  Observatory  in  1676. 
His  method  may  be  understood  from  the  accompanying 
diagram  in  which  5  may  stand  for  the  Sun,  the  circle 


FIG.  90. 


ABCD  for  the  Earth's  orbit,  J  for  the  planet  Jupiter, 
and  M  for  the  largest  of  Jupiter's  five  moons,  known 
as  the  "first  satellite."  This  moon  revolves  about 
Jupiter  and  is  eclipsed  at  equal  intervals  of  time  by 
passing  into  the  shadow  of  the  planet.  The  time  of 


OPTICS  AND   RADIATION  331 

rotation,  and  hence  the  period  between  two  successive 
eclipses,  is  48  hours  28  minutes  35  seconds.  Roemer 
found  that  when  the  Earth  was  at  A  or  C  the  ob- 
served time  between  two  successive  eclipses  was  the 
same,  but  that  when  the  Earth  was  approaching 
Jupiter,  as  at  I),  the  eclipses  occurred  at  shorter  inter- 
vals, and  when  the  Earth  was  receding-  from  Jupiter, 
as  at  By  the  intervals  between  successive  eclipses  were 
greater  than  when  the  Earth  was  at  A  or  C.  Roemer 
reasoned  from  this  observation  that  it  took  light  an 
appreciable  interval  of  time  to  travel  the  distance 
passed  over  by  the  Earth  in  the  time  which  elapsed 
between  two  successive  eclipses.  By  acting  on  this 
conclusion  and  carefully  noting  the  time  between  two 
successive  eclipses  when  the  Earth  was  at  A  and 
neither  approaching  nor  leaving  Jupiter,  the  exact 
time  at  which  an  eclipse  would  occur  six  months  later 
when  the  Earth  would  be  at  C  was  calculated.  By 
observing  the  time  of  this  eclipse  six  months  later,  it 
was  found  to  occur  i6£  minutes  later  than  the  calcu- 
lated time,  while  the  time  between  two  successive 
eclipses  was  the  same  as  when  the  Earth  was  at  A. 
It  was  accordingly  concluded  that  light  required  i6£ 
minutes  to  travel  across  the  Earth's  orbit  from  A  to  C. 

Calling  the  diameter  of  the  Earth's  orbit  296,000,000 
kilometers  or  186,000,000  miles,  and  the  time  required 
for  light  to  cross  it  990  seconds,  this  calculation  makes 
the  velocity  of  light  about  299,000,000  meters,  or 
188,000  miles,  a  second. 

In  more  recent  times  several  methods  have  been 
devised  for  measuring  directly  the  velocity  of  light. 
As  a  result  of  many  careful  measurements,  the  velocity 
is  now  taken  ^is  about  300,000,000  meters  a  second. 


332  PHYSICS 

First  Law  of  Light  Propagation. — We  have  already 
defined  (page  129)  as  isotropic  those  substances  in  which 
all  the  physical  properties  are  the  same  in  all  directions. 
Since  the  possibility  of  transmitting  light  is  regarded 
as  a  physical  property,  it  follows  that  in  an  isotropic 
medium  the  velocity  of  light  is  the  same  in  all  directions 
from  its  source.  This  may  be  regarded  as  the  first  law 
of  light  propagation. 

Since  all  liquids  and  gases,  as  well  as  amorphous 
solids,  are  isotropic,  the  velocity  of  light  is  the  same 
in  all  directions  from  its  source  in  these  substances. 

Light  Waves. — If  a  luminous  point  should  suddenly 
come  into  existence  in  an  isotropic  optical  medium,  the 
illuminated  region  about  the  point  at  any  instant  after 
the  origin  of  the  light  would  be  a  sphere  with  the 
luminous  point  as  its  center.  In  one  second  after  the 
origin  of  the  light  this  illuminated  region  would  be  a 
sphere  with  a  radius  of  300,000,000  meters.  In  one 
three-hundred-millionth  of  a  second  it  would  be  a 
sphere  with  a  radius  of  one  meter.  A  disturbance 
propagated  as  a  constantly  enlarging  sphere  is  called 
a  Spherical  Wave.  We  may  accordingly  state  the  first 
law  of  light  propagation  in  other  words  by  saying, 
Light  is  propagated  in  spherical  waves. 

Wave-front. — The  term  Wave-front  is  used  as  in 
Sound.  Thus  the  whole  surface  of  a  spherical  wave  at 
any  given  instant  of  time  is  called  a  Wave- front. 

Law  of  Decrease  of  Intensity. — If  the  surface  of  a 
spherical  wave  of  light  has  at  all  times  the  same  total 
illumination,  then  the  intensity  of  illumination  will 
decrease  as  the  area  of  the  wave-front  increases.  Since 
the  surface  of  a  sphere  increases  as  the  square  of  its 
radius,  the  intensity  of  illumination  upon  tJie  spherical 


OPTICS  AND   RADIATION  333 

wave-front  of  light  must  decrease  as  the  square  of  the 
radius  of  tJie  spherical  wave  increases. 

If  a  screen  be  placed  near  a  source  of  light  to  inter- 
cept a  portion  of  the  wave-front,  the  intensity  of 
illumination  upon  the  screen  will  vary  with  its  distance 
from  the  source  of  light.  At  a  distance  of  two  feet 
from  the  source  it  will  have  only  one  fourth  the  intensity 
of  illumination  that  it  would  have  at  a  distance  of  one 
foot.  The  illumination  tipon  the  screen  will  decrease  as 
the  square  of  its  distance  from  the  source  of  light 
increases.  ~ 

PHOTOMETRY 

Definitions. — That  branch  of  Optics  which  is  con- 
cerned with  the  measurement  of  light  intensities  is 
called  Photometry.  An  instrument  used  to  compare 
intensities  of  illumination  is  called  a  Photometer. 
Many  different  forms  of  photometer  are  made.  Some 
of  the  more  common  ones  are  described  below. 

The  Rumford  Photometer. — Rumford's  Photometer 
is  made  by  placing  an  upright,  opaque  rod,  as  a  lead- 
pencil,  at  a  distance  of  8  or  10  centimeters  in  front  of 
a  vertical  sheet  of  un glazed  white  paper,  which  should 
be  mounted  against  a  board.  This  apparatus  is  set  up 
in  a  dark  room  and  a  lighted  candle  or  lamp  is  placed 
in  front  of  it  so  that  the  shadow  of  the  rod  will  fall  upon 
the  paper.  The  whole  paper  with  the  exception  of  this 
shadow  will  be  illuminated  by  the  light.  If  another 
lamp  or  candle  be  placed  beside  the  first  one,  two 
shadows  will  be  thrown  upon  the  screen,  but  neither  of 
them  will  be  as  dark  as  the  first  one,  since  the  shadow 
cast  by  each  light  will  be  illuminated  by  the  other  light. 
All  the  rest  of  the  screen  will  be  illuminated  by  both 


334  PHYSICS 

lights.  If  the  lights  are  placed  so  that  the  shadows 
are  very  near  together,  it  will  be  possible  to  adjust  the 
distances  of  the  lights  so  that  the  two  shadows  seem  to 
be  equally  dark.  This  will  be  the  case  when  each 
shadow  is  equally  illuminated  by  the  other  light.  The 
intensities  of  illumination  of  the  two  lights  upon  the 
screen  will  then  be  the  -same,  and  the  intensity  of 
illumination  of  either  shadow  will  be  just  half  the 
intensity  upon  the  rest  of  the  screen. 

The  Bunsen  Photometer. — Bunsen's  Photometer  is 
made  by  putting  a  drop  of  grease  on  a  piece  of  unglazed 
white  paper  and  placing  the  paper  vertical  between  the 
two  lights  to  be  compared,  with  one  face  turned  toward 
each  light.  The  grease  spot  on  the  paper  is  more 
transparent  than  the  rest  of  the  paper  and  allows  part 
of  the  light  to  pass  through  the  paper.  If  the  paper 
be  lighted  from  only  one  side,  the  grease  spot  wilj 
seem  darker  than  the  rest  of  the  paper  when  looked  at 
from  the  light  side  and  lighter  when  looked  at  from  the 
dark  side.  When  both  sides  of  the  paper  are  equally 
illuminated  so  that  as  much  light  passes  through  the 
paper  from  one  side  as  from  the  other,  the  grease  spot 
will  appear  of  the  same  brightness  as  the  rest  of  the 
paper,  and  the  relative  intensities  of  the  two  lights  can 
be  calculated  from  their  distance  from  the  paper.  In 
practice,  the  grease  spot  cannot  be  made  of  the  same 
brightness  as  the  rest  of  the  paper  on  both  sides  at 
once,  since  some  of  the  light  is  absorbed  in  passing 
through  the  paper.  When  the  proper  adjustment  has 
been  made,  the  grease  spot  will  accordingly  appear  a 
little  darker  than  the  rest  of  the  paper  on  both  sides. 

The  Joly  Photometer. — This  photometer  is  made  by 
cutting  out  two  little  slabs  of  paraffin  about  a  centi- 


HE  ^ 

UNIVERSITY   1 

cAl  /OPTICS  AND  RADIATION  335 

meter  thick  and  of  convenient  length  and  width 
(5  centimeters  long  and  2  centimeters  broad  gives  a 
convenient  size),  and  by  warming  one  side  of  each  and 
sticking  them  together  with  a  piece  of  black  paper  or 
tin-foil  between  them  to  form  an  opaque  partition. 
The  two  slabs  should  be  of  the  same  thickness. 

This  instrument  is  placed  between  the  two  lights 
whose  intensities  are  to  be  compared,  with  the  opaque 
partition  vertical,  like  the  screen  of  the  Bunsen  Photom- 
eter. The  translucent  slabs  of  paraffin  are  then  each 
illuminated  by  one  light  and  shielded  from  the  other. 
When  they  are  equally  bright  as  seen  from  their  edges, 
the  adjustment  is  complete,  and  the  distances  of  the 
lights  may  be  measured. 

Comparison  of  Photometers. 

LABORATORY  EXERCISE  120. — Place  two  lighted  candles 
about  a  meter  apart,  and  place  a  Bunsen  or  Joly  photometer 
between  them,  adjusting  it  so  that  both  lights  give  equal 
illumination  at  the  photometer.  Measure  the  distance  to 
one  of  the  candles,  and  without  disturbing  anything  else 
remove  this  candle  and  replace  it  where  it  seems  to  give  the 
same  illumination  as  before.  Measure  the  distance  again, 
and  see  how  nearly  you  have  placed  it  in  the  original  posi- 
tion. Repeat  three  or  four  times,  and  find  the  greatest 
variation  between  your  settings. 

Make  the  same  test  with  one  or  more  of  the  other  pho- 
tometers and  decide  which  is  the  more  sensitive  instrument. 

What  part  of  the  whole  distance  of  the  candle  from  the 
photometer  was  uncertain  in  your  settings  ? 

What  percentage  of  the  whole  distance  was  uncertain  ? 

To  Test  the  Law  of  Inverse  Squares. 

LABORATORY  EXERCISE  121.* — Set  up  a  photometer  in  a 
dark  room,  place  a  lighted  candle  about  50  centimeters  from 
it  and  place  four  lighted  candles  mounted  on  a  block  so  that 

*  Any  of  the  above  photometers  may  be  used  in  this  experiment.  It 
may  be  well  to  have  different  members  of  the  class  use  different  instru- 
ments. 


336  PHYSICS 

they  will  all  be  in  a  line  perpendicular  to  the  photometer 
screen  and  at  such  a  distance  from  the  photometer  that  their 
illumination  at  the  instrument  will  be  equivalent  to  that  of 
the  single  candle.  Measure  this  distance  to  a  point  between 
the  two  inner  candles.  Repeat  with  the  single  candle  25 
centimeters  from  the  photometer. 

What  is  the  ratio  between  the  distances  of  the  two  sources 
of  light  ?  What  should  be  the  ratio  according  to  the  law  of 
inverse  squares  ?  (It  is  evident  that  in  this  experiment  the 
four  candles  should  be  like  the  single  candle,  and  their  wicks 
should  all  be  trimmed  to  as  nearly  the  same  height  as 
possible.) 

How  far  from  the  screen  should  two  candles  be  placed  to 
give  the  same  illumination  as  one  candle  at  25  centimeters  ? 
Place  two  candles  at  this  distance  and  compare  them  with 
the  single  candle. 

Are  the  variations  of  your  results  from  the  law  of  inverse 
squares  greater  than  the  variations  between  single  compari- 
sons of  two  lights  ?  If  so,  what  may  be  the  possible  causes 
of  error  ? 

Candle-power  of  a  Lamp. 

LABORATORY  EXERCISE  122. — The  intensity  of  different 
artificial  sources  of  light  is  generally  measured  in  candle- 
powers.  A  lamp  is  said  to  be  of  ten  candle-power  when  it 
gives  as  much  light  as  ten  standard  candles.* 

Using  an  ordinary  candle  as  a  standard,  determine  the 
candle-power  of  a  kerosene  lamp.  Make  five  determina- 
tions with  the  candle  at  different  distances  and  take  the 
mean  of  the  results. 

Letting  C  represent  the  illuminating  power  of  a  lamp,  c 
that  of  a  candle,  and  D  and  d  the  corresponding  distances 
from  a  screen  which  is  equally  illuminated  by  both,  .give  an 
equation  for  the  candle-power  of  the  lamp  =  C  in  terms  of 
c,  D.  and  d. 

*  The  standard  candle  is  different  in  different  countries.  In  England 
it  is  a  sperm  candle  weighing  six  to  the  pound  and  burning  at  the  rate 
of  1 20  grains  per  hour.  In  Germany  it  is  a  paraffin  candle  of  uniform 
diameter  of  two  centimeters,  with  its  wick  trimmed  so  that  the  flame  is 
five  centimeters  high.  The  British  standard  is  generally  used  in  this 
country.  No  candle  is  an  accurate  light  standard,  as  the  light  con- 
stantly fluctuates  in  brightness. 


OPTICS  AND  RADIATION  .337 

(It  is  advised  that  students  test  the  candle-power  of  the 
lights  used  in  their  homes  by  means  of  the  Joly  photometer.) 

What  difficulty  appears  in  comparing  a  candle  with  a  lamp 
which  gives  a  very  white  light  ? 

PROBLEMS. — A  standard  candle  is  placed  2  feet  from  a 
screen  and  a  lamp  of  nine  candle-power  is  placed  3  feet 
from  the  screen.  Compare  their  illuminating  power  on  the 
screen. 

A  standard  candle  and  a  i6-candle-power  lamp  are  placed 
2  meters  apart.  Where  between  them  must  a  Joly  photom- 
eter be  placed  to  show  equal  illumination  on  both  sides  ? 

In  measuring  the  distance  of  a  candle  from  a  Rumford 
photometer,  do  you  measure  from  the  candle  to  its  shadow, 
or  to  the  shadow  which  it  illuminates  ? 

Two  8-candle-power  lamps  are  placed  on  opposite  sides 
of  a  Bunsen  photometer  screen,  one  20  centimeters  and  the 
other  30  centimeters  from  the  screen.  Where  must  a  stand- 
ard candle  be  placed  to  make  the  illumination  on  both  sides 
of  the  screen  the  same  ? 

REFLECTION   OF   LIGHT 

Reflective  Power  of  Various  Bodies.— Place  an  open 
book  with  its  back  to  a  window  or  other  source  of  light 
so  that  the  printed  pages  will  be  in  the  shadow.  Try 
to  reflect  light  upon  the  pages  by  means  of  a  mirror. 
By  means  of  a  piece  of  window  glass.  Of  white  paper. 
Of  black  paper.  Do  these  bodies  reflect  light  ?  Do 
they  reflect  equally  well  ? 

Luminous  bodies  are  made  visible  by  the  light  which 
they  emit;  non-luminous  bodies  by  the  light  which 
they  reflect.  A  body  which  reflects  no  light  to  the  eye 
is  invisible.  Its  surface  appears  black. 

Regular  and  Irregular  Reflection. — There  are  two 
ways  in  which  bodies  may  reflect  light.  They  may 
reflect  the  light  so  that  we  can  see  plainly  the  surface 
of  the  body  itself,  as  is  the  case  with  white  paper,  or 


338  PHYSICS 

they  may  reflect  the  light  so  that  we  see  the  original 
source  of  light  instead  of  the  reflecting  body,  as  in 
reflection  from  a  mirror.  In  the  former  case  light  goes 
off  in  all  directions  from  each  point  in  the  reflecting 
body  as  from  an  original  source  of  light;  in  the  latter 
case  the  light  is  reflected  only  in  a  definite  direction 
from  each  part  of  the  reflecting  surface.  The  former 
is  called  irregular  or  diffuse  reflection;  the  latter  is 
called  regular  or  mirror  reflection.  It  is  only  by 
diffuse  reflection  that  non-luminous  bodies  are  made 
visible.  A  perfectly  reflecting  mirror  surface  would  be 
invisible  to  us,  and  we  would  see  in  it  only  the  bodies 
whose  light  it  would  reflect  to  our  eyes. 

Effect  of  Polishing  Surface  of  Reflecting  Body.— In 
general,  when  light  falls  upon  a  non-luminous  body 
part  of  it  is  reflected.  The  more  highly  polished  the 
surface  of  the  reflecting  body,  the  greater  the  propor- 
tion of  the  light  which  is  regularly  reflected.  Almost 
any  surface  may  be  made  a  mirror  surface  by  sufficient 
polishing. 

Huyghens'  Construction  for  Advancing  Wave-front. 
— In  order  to  understand  the  nature  of  reflection  it  is 
necessary  to  consider  more  fully  the  method  of  light 
propagation. 

The  method  of  wave  propagation  in  an  elastic 
medium  such  as  the  Luminiferous  Ether  is  supposed  to 
be  is  by  each  point  on  the  surface  of  the  spherical  wave 
becoming  the  center  of  disturbance  from  which  a 
secondary  spherical  wave  is  sent  off.  The  points  in 
the  surface  of  these  secondary  waves  become  new 
centers  of  disturbance  from  which  other  waves  start, 
and  so  on  indefinitely.  Since  all  these  secondary 
waves  increase  at  the  same  rate,  the  resulting  surface 


OPTICS  AND  RADIATION 


339 


tangent  to  all  of  them  is  itself  spherical  and  becomes 
the  main  wave-front  which  we  consider  in  light  propa- 
gation. 

The  method  of  wave  propagation  just  described  may 
be  better  understood  from  a  consideration  of  Fig.  91. 
— If  5  represent  a  source  of 
light,  the  circle  WF  will  repre- 
sent a  section  of  the  spherical 
wave-front  at  a  given  instant  of 
time.  If  the  points  a,  b,  c,  etc., 
in  the  main  wave-front  be  re- 
garded as  centers  of  spherical 
waves,  the  wave-fronts  of  these 
spherical  waves  will  at  another 
given  instant  of  time  combine 
to  form\a  new  wave-front,  as 
W'F' .  This  method^pf  drawing  the  projection  of  an 
advancing  wave-front  is  known  as  Huyghens'  Con- 
struction. 

While  these  secondary  wave-fronts  are  in  reality  im- 
measurably small,  we  can  use  them  in  projecting  a 
wave-front  as  if  they  were  of  sensible  size.  Thus  in 
the  figure  we  may  project  secondary  wave-fronts  from 
a,  b,  c,  etc.,  with  any  desired  radius,  and  the  resulting 
circle  tangent  to  the  secondary  wave-fronts  will  accu- 
rately represent  a  projection  of  the  main  wave-front  at 
some  given  instant  of  time.  It  is  by  means  of  these 
secondary  wave-fronts  that  we  are  enabled  to  project 
the  main  wave-front  after  it  has  been  reflected  from  a 
given  surface. 


FIG.  91. 


340 


PHYSICS 


REFLECTION   FROM   PLANE   SURFACES 

Reflection  from  Plane  Mirror. — In  Fig.  92  let  MR 
be  the  trace  of  a  mirror  surface  and  5  a  source  of  light. 
The  dotted  line  ABC  will  then  represent  a  section  of 
a  wave-front  from  5  as  it  would  have  been  at  a  given 
instant  with  the  mirror  removed.  Since  the  light  is 
reflected  from  MR,  each  point  on  the  surface  of  MR 
may  be  regarded  as  the  center  of  a  secondary  wave 
moving  back  toward  5.  The  radii  of  these  waves  may 
be  known  if  we  know  the  relative  velocities  of  the 


FIG.  92. 

incident  and  reflected  light.  If  the  velocity  of  the 
reflected  light  be  taken  the  same  as  the  velocity  of  the 
incident  light,  the  secondary  wave  from  a  will  have 
returned  to  D  in  the  time  which  would  have  been 
required  for  the  advancing  wave  to  reach  B.  The 
radius  of  the  secondary  wave  from  a  will  accordingly 
be  aB.  In  the  same  way  the  radius  of  the  secondary 
wave  from  b  will  be  bo,  from  c,  en,  and  the  like. 


OPTICS  AND  RADIATION  341 

Drawing  these  secondary  wave-fronts,  the  curved  line 
ADC  which  is  tangent  to  all  of  them  will  represent  a 
projection  of  the  main,  reflected  wave-front. 

Draw  a  figure  showing  the  projection  of  a  spherical 
wave-front  reflected  from  a  plane  mirror  surface,  as 
above,  and  show  by  construction  that  the  reflected 
wave-front  is  also  spherical  and  has  its  center  at  a  point 
Sf  as  far  back  of  the  mirror  as  5  is  in  front. 

Virtual  Image  by  Reflection  from  Plane  Mirror. — 
To  an  observer  whose  eye  receives  a  part  of  the 
reflected  wave-front  the  source  5  will  appear  to  be  back 
of  the  mirror  at  Sf .  The  point  S/  is  accordingly  called 
the  virtual,  or  apparent,  image  of  5.  It  is  called  the 
virtual  image  because  in  reality  there  is  no  source  of 
light  back  of  the  mirror. 

To  Locate  the  Virtual  Image  of  a  Plane  Mirror. 

LABORATORY  EXERCISE  123.  (One  or  all  of  the  following 
methods  may  be  used. ) 

(i)  A  piece  of  mirror  about  five  or  six  inches  long  and 
having  at  least  one  straight  edge  has  several  ink  lines  drawn 
perpendicular  to  the  straight  edge  and  about  an  inch  apart. 
Place  the  mirror  on  the  straight  edge  on  a  sheet  of  paper,  rest- 
ing it  against  a  block  or  other  support  so  that  it  will  stand 
upright.  The  ink  lines  will  then  be  vertical.  Draw  a  pencil 
line  on  the  paper  showing  the  edge  of  the  mirror  and  mark 
with  the  pencil  point  the  foot  of  each  ink  line  upon  the 
paper.  Thus  in  Fig.  93  let  MR  represent  the  trace  of  the 
mirror  edge  and  Z15  Z2,  etc.,  the  positions  of  the  ink  lines. 

Stick  a  pin  upright  in  front  of  the  mirror,  as  at  P. 
Then  holding  the  eye  near  the  paper,  stick  other  pins,  as 
PI}  P2,  etc.,  where  they  will  appear  in  straight  lines  with 
the  ink  marks  Llt  Z2,  etc.,  and  the  image  of  P.  Remove 
the  mirror,  and  by  means  of  a  ruler  and  pencil  draw  the 
straight  lines  PlLl,  P-z^2>  etc->  producing  them  back  of  the 
surface  of  the  mirror  until  they  meet.  If  carefully  drawn, 
they  will  all  meet  at  one  point  back  of  the  mirror  where  the 
image  of  P  seemed  to  be,  Let  Q  represent  this  point  Q\ 


342 


PHYSICS 


intersection  and  determine  by  measurement  if  it  lies  in  a 
perpendicular  from  P  through  the  mirror,  and  is  as  far  back 
of  the  mirror  as  P  is  in  front. 


FIG.  93. 

(2)  Place  a  mirror  MR  upright  on  a  sheet  of  paper,  as 
before.  Place  a  lighted  candle  at  C  and  stick  two  hat-pins 
or  knitting-needles  upright  at  Pl  and  Pa. 

M 


R 

FIG.  94. 

Each  of  these  pins  will  have  two  shadows,  one  caused  by 
the  candle  and  the  other  by  the  reflected  light  from  the 
mirror.  Lay  a  ruler  along  the  shadows  and  trace  them  upon 


OPTICS  AND  RADIATION 


343 


the  paper.  One  pair  of  these  lines  produced  will  meet  at 
the  candle  and  the  other  pair  at  its  virtual  image  back  of  the 
mirror.  Locate  this  image,  and  answer  the  question  as 
above. 

(3)  Set  a  pane  of  glass  vertical  in  a  darkened  room  and 
place  a  lighted  candle  in  front  of  it.  Set  an  unlighted 
candle  back  of  the  glass  so  that  when  seen  through  the  glass 
it  appears  to  coincide  in  position  with  the  image  of  the 
lighted  candle.  Determine  as  above  the  position  of  the 
image  relative  to  the  surface  of  the  glass. 

As  a  result  of  your  experiments,  state  the  law  of  location 
of  a  virtual  image  seen  by  reflection  from  a  plane  mirror. 
Thus,  A  source  of  light  in  front  of  a  plane  mirror  has  its 
virtual  image,  etc. 

Can  you  conclude  from  the  location  of  this  image  whether 
the  incident  and  reflected  lights  travel  with  the  same 
velocity  ? 

Referring  to  Fig.  92,  if  the  velocity  of  the  incident  light 
were  greater  than  that  of  the  reflected  light,  would  the 
reflected  wave-front  be  more  or  less  convex  than  the  inci- 
dent wave-front  ?  Would  this  make  S'  appear  nearer  to  or 
farther  from  the  mirror  than  £  ? 

Since  only  a  portion  of  the  incident  light  is  reflected,  the 


Si- 


R 


-itf 


FIG.  95. 


FIG.  96. 


intensity  of  the  reflected  light  is  less  than  that  of  the  incident 
light.  Does  the  velocity  of  light  apparently  depend  upon 
its  intensity  ? 

Give  a  rule  for  locating  the  virtual  image  of  a  point  as  seen 
by  reflection  from  a  plane  mirror. 


344  PHYSICS 

Give  a  rule  for  locating  the  image  of  an  object  composed 
of  many  points. 

Letting  MR,  Fig.  95,  represent  the  projection  of  a  mirror 
surface,  draw  the  image  of  the  arrow  ab  in  the  position  in 
which  it  will  appear.  How  will  the  object  and  i^s  image 
compare  in  size  ? 

Letting  S,  Fig.  96,  represent  the  location  of  a  source  of 
light  and  Sf  its  virtual  image  as  seen  in  the  plane  mirror 
MRt  prove  by  Geometry  that  lines  drawn  from  S  and  S'  to 
any  point  in  the  mirror  surface  make  equal  angles  with  MR. 

Draw  a  perpendicular  through  MR  at  the  point  of  meet- 
ing of  the  two  lines,  and  prove  that  the  lines  from  S  and  S' 
make  equal  angles  with  this  perpendicular. 

The  Method  of  Rays. — In  the  earlier  theory  of 
Optics,  known  as  the  Emission  Theory,  light  was  sup- 
posed to  consist  of  small  particles  of  a  peculiar  sub- 
stance sent  out  from  the  luminous  body.  These 
particles  were  supposed  to  travel  in  straight  lines 
through  an  isotropic  medium,  but  to  have  their  direc- 
tion changed  by  reflection  or  by  parsing  from  one 
medium  into  another. 

The  paths  followed  by  these  particles  were  called 
Rays.  A  number  of  parallel  rays  were  called  a  Beam, 
and  a  number  of  diverging  or  converging  rays  were 
called  a  Pencil. 

We  now  know  that  no  such  particles  exist,  but  the 
terms  ray,  beam,  and  pencil  of  light  are  still  used. 
Thus  a  straight  line  drawn  from  a  luminous  point  to 
the  surface  of  its  spherical  wave  is  still  called  a  ray. 
It  is,  in  fact,  a  radius  of  the  spherical  wave. 

In  the  language  of  rays,  we  see  a  luminous  or  illumi- 
nated point  by  means  of  a  diverging  pencil  of  rays 
which  enter  the  eye  from  that  point.  As  a  matter  of 
fact,  we  see  the  point  by  means  of  a  small  circular  area 
of  its  wave-front  which  enters  the  pupil  of  the  eye. 


OPTICS  AND  RADIATION 


345 


The  radii  drawn  from  the  visible  point  to  this  area  of 
the  wave-front  are  the  rays  which  make  up  the  diverg- 
ing pencil  spoken  of  in  the  language  of  the  Emission 
Theory.  Thus  in  Fig.  97  the  radii  Sa,  Sb,  and  the 


FIG.  97. 

like,  drawn  from  5  to  the  pupil  of  the  eye  may  represent 
the  diverging  pencil  of  rays  by  which  we  are  said  to 
see  the  body. 

In  the  case  of  reflected  light,  a  small  segment  of  the 
wave-front  enters  the  eye  after  its  direction  has  been 
changed  by  reflection.  Thus  if  MR,  in  Fig.  98,  repre- 


O    x*^ 

OK- 


FIG.  98. 

sent  the  reflecting  surface,  S  the  source  of  light,  and 
S'  its  virtual  image,  the  segment  of  the  wave-front 
entering  the  eye  appears  to  have  its  source  at  S1 ',  and 
the  pencil  of  rays  seems  to  be  S'ca,  S'db,  etc.,  instead 
of  the  broken  lines  Sea  and  Sdb. 


346  PHYSICS 

In  the  language  of  the  older  Optics,  the  rays  were 
bent  at  the  surface  of  the  mirror. 
The  rays  Sc  and  Sd  were  called 
incident  rays,  and  the  rays  ca  and 
db  were  called  reflected  rays. 
The  oldest  known  law  of  reflec- 
tion and  the  one  upon  which  the 
Geometrical  Optics  of  2000  years 
ago  was  based  may  be  stated  as 
follows :  The  incident  and  reflected 
rays  make  equal  angles  with  a  perpendicular  to  the 
mirror  at  the  point  of  reflection.  Prove  this  proposition 
geometrically  by  the  use  of  Fig.  99,  letting  i  equal  the 
angle  of  incidence  and  r  the  angle  of  reflection. 

Multiple  Reflection  by  a  Mirror. — Set  a  pane  of 
thick  glass  on  edge  and  note  that  two  images  of  a 
lighted  candle  may  be  seen  by  reflection  from  it.  One 
of  these  reflections  takes  place  when  the  light  wave 
enters  the  glass  from  the  air,  and  the  other  when  the 
light  wave  emerges  from  the  glass  into  the  air  again. 
In  a  very  highly  polished  glass  plate  several  images 
may  be  seen  by  reflection  of  some  of  the  light  at  each 
emergence  from  the  glass. 

REFLECTION    FROM   CURVED   SURFACES 

Projection  of  a  Wave-front  Reflected  from  a  Curved 
Surface. — The  method  of  projecting  a  reflected  wave- 
front  by  means  of  its  secondary  wave-fronts  enables  us 
to  determine  the  shape  of  a  wave-front  reflected  from 
a  surface  of  any  curvature. 

The  only  curved  reflecting  surfaces  usually  considered 
in  an  elementary  study  of  Optics  are  spherical  surfaces. 


OPTICS  AND   RADIATION 


347 


Reflection  from  Convex   Spherical   Surfaces. — In 

Fig.  100  is  shown  the  projection  of  a  spherical  wave- 
front  from  the  point  5  after  reflection  from  the  convex 
spherical  mirror  MR.  It  will  be  seen  that  the  reflected 
wave-front  BFD  is  more  convex  than  the  incident 
wave-front  ABCDE,  and  that  S' ,  the  virtual  image  of 
5,  is  much  nearer  the  mirror  surface  than  5. 

Draw  on  a  conveniently  large  scale  the  projection  of  a 
spherical  wave-front  reflected  from 
a  convex  spherical  surface,  as  in 
Fig.  100,  and  determine  by  con- 
struction whether  the  reflected 
wave-front  is  perfectly  or  only 
approximately  spherical. 

Will  all  parts  of  this  reflected 
wave-front  seem  to  come  from  the 
same  point,  S'  ? 

Will    the    virtual    image  of 
point  *$"  be  a  point  or  a  blur  ? 

Images  Seen  by  Reflection 
from  a  Convex  Surface. 

Observe  the  images  of  various 
objects  seen  by  reflection  from  a 
polished  metal  ball  or  other  con- 
vex, spherical  surface. 

Are    the    images    nearer    to    or  FIG.  100.     , 

farther  from  the  reflecting  surfaces  than  the  objects  ? 

Are  they  larger  or  smaller  than  the  objects  ? 

Are  they  erect  or  inverted  ? 

Look  at  the  image  of  your  face  in  such  a  mirror.  Is  the 
image  distorted  ? 

Reflection  of  Plane  Wave-front  from  Convex 
Spherical  Surface. — We  have  seen  that  the  wave-front 
of  the  sunlight  at 'the  Earth  is  the  surface  of  a  sphere 
of  93,000,000  miles  radius.  Such  a  surface  cannot  be 
distinguished  from  a  plane  surface,  and  we  accordingly 


343 


PHYSICS 


speak  of  the  sunlight  as  having  a  plane,  or  flat,  wave- 
front. 

In  Fig.  10 1  let  MR  be  a  convex  spherical  mirror 
and  WF  a  plane  wave-front  advanc- 
ing from  left  to  right,  the  dotted  line 
representing  the  position  which  the 
wave-front  would  have  occupied  with 
the  mirror  removed.  Several  of  the 
radii  to  the  plane  wave-front  are 
drawn,  and  the  secondary  wave- 
fronts  from  the  points  where  these 
radii  meet  the  mirror  surface.  The 
reflected  wave-front  will  be  tangent 
to  these  secondary  wave-fronts. 

Draw  the  figure  to  a  convenient  scale, 
including  the  projection  of  the  reflected 
FIG   101  wave-front,   and  determine  whether  this 

wave-front  is  spherical. 

Locate  the  center  of  curvature  of  the  mirror  and  the  point 
from  which  the  reflected  wave-front  seems  to  diverge. 
Measure  the  distance  back  of  the  mirror  to  each  of  these 
points  and  determine  whether  any  simple  relation  exists 
between  these  two  distances. 

How  should  the  image  of  the  Sun  appear  when  seen  by 
reflection  from  the  convex  surface  of  a  spherical  mirror  ? 

How  far  back  of  the  mirror  surface  should  the  image 
appear  ? 

Observe  the  image  of  the  Sun  in  such  a  mirror  and  deter- 
mine whether  your  conclusions  are  verified. 

Reflection  from  Concave  Spherical  Surfaces. — We 
have  seen  that  reflection  from  a  convex  surface  always 
makes  the  wave-front  more  convex  than  the  incident 
wave-front.  In  reflection  from  a  concave  surface  the 
opposite  is  true.  Thus  the  reflecting  surface  may  be 
said  to  impress  its  own  form  upon  the  wave-front. 


OPTICS  AND   RADIATION 


349 


FIG.  102. 


In  Fig.  1 02  let  WF  be  a  wave-front  from  5  reflected 
from  the  concave  surface  MR.  It  will 
be  seen  from  the  projection  that  the 
reflected  wave-front  is  much  less  con- 
vex than  the  incident  wave-front.  It 
will  also  be  seen  that  the  reflected 
wave-front,  if  drawn  tangent  to  the 
secondary  reflected  wave-fronts,  is  not 
perfectly  spherical. 

Since  reflection  from  a  concave  sur- 
face renders  the  reflected  wave-front 
less  convex,  it  follows  that  a  plane 
wave-front  reflected  from  a  concave 
surface  will  be  made  concave  by 
reflection. 

If  the  reflecting  surface  impresses  its  form  upon  the 
reflected  wave-front,  a  plane  wave-front  reflected  from 
a  concave  spherical  surface  should  become  a  spherical, 
concave  wave-front. 

Since  a  convex  wave-front  grows  larger  as  it 
advances,  a  concave  wave-front  should  contract  as  it 
advances,  and  if  it  is  a  spherical,  concave  wave-front, 
it  should  contract  to  a  point.  A  portion  of  the  Sun's 
wave-front  reflected  from  a  concave,  spherical  mirror 
should  accordingly  contract  toward  a  point. 

Contraction  of  Concave  Wave-front. 
LABORATORY  EXERCISE  124. — Allow  a  beam  of  sunlight  to 
pass  through  a  circular  hole  five  or  six  centimeters  in 
diameter  and  to  fall  upon  a  spherical,  concave  mirror.  By 
tapping  together  two  blackboard  erasers  above  the  beam  and 
thus  filling  the  air  with  particles  of  chalk  dust  or  by  filling 
the  air  with  smoke  the  path  of  the  sunbeam  can  be  traced 
through  the  room.  Turn  the  mirror  so  that  the  reflected 
beam  will  make  an  angle  with  the  incident  beam,  and  try  to 
make  its  path  visible  by  means  of  the  chalk  dust  or  smoke. 


350  PHYSICS 

Does  the  reflected  beam  contract  to  a  point  ?  What  must 
be  the  shape  of  its  wave-front  when  it  is  first  reflected  from 
the  mirror  ? 

What  must  be  the  shape  of  its  wave-front  after  it  has 
passed  the  point  of  greatest  contraction  ? 

Hold  a  piece  of  paper  in  the  path  of  the  reflected  beam 
and  at  different  distances  from  the  mirror.  Where  is  the 
intensity  of  the  illumination  upon  the  paper  greatest  ?  Are 
the  heat  effects  also  more  intense  at  this  point  ? 

Focus  of  Concave  Wave-front. — The  center  to  which 
a  concave  wave-front  contracts  is  called  its  Focus. 

Focal  Length  of  Concave  Mirror. — The  distance 
from  a  concave  mirror  to  the  point  at  which  a  plane 
wave-front  will  be  brought  to  a  focus  is  called  the 
Focal  Length  of  the  mirror. 

Measure  the  focal  length  of  the  mirror  used  to  bring  the 
sunlight  to  a  focus. 

Relation  of  Focal  Length  to  Radius  of  Curvature. 

— By  remembering  that  lines  drawn  from  an  object  and 
its  image  make  equal  angles  with  the  reflecting  surface, 
or,  in  the  language  of  rays,  that  the  angles  of  incidence 
and  reflection  are  equal,  we  may  establish  by  Geometry 
a  relation  between  the  focal  length  and  the  radius  of 
curvature  of  a  concave,  spherical  mirror. 

Thus  in  Fig.  103  let  C  represent  the  center  of 
curvature  and  F  the  focus  for  a  plane  wave-front  (called 
the  Principal  Focus)  of  the  mirror  MR.  If  AB  repre- 
sent an  incident  ray  parallel  to  CE,  BD  will  represent 
the  reflected  ray  from  the  point  B.  Since  CB  is  a 
normal  to  the  reflecting  surface,  angle  ABC  —  angle  i 
and  CBF  =  angle  r.  We  accordingly  have  the  follow- 
ing relations  between  the  angles  shown  in  the  figure: 
i  =  r\  i  —  a\  hence  a  =  r,  and  triangle  CBF  is 
isosceles  and  side  CF  =  side  FB.  If  B  be  taken  very 


OPTICS  AND  RADIATION  351 

near  E,  the  center  of  the  mirror,  FB  —  FE,  nearly, 
and  the  focal  length  FE  is  approximately  half  of  CE. 
It  is  accordingly  customary  to  regard  the  focal  length 
of  a  concave  mirror  as  one  half  its  radius  of  curvature. 


A 


FIG.  103. 

Spherical  Aberration. — We  have  seen  that  a  plane 
wave-front  reflected  from  a  concave  spherical  mirror  is 
not  made  perfectly  spherical  by  reflection,  hence  it  will 
not  all  contract  to  the  same  focus.  This  can  also  be 
seen  from  Fig.  103.  Since  BF  always  equals  CF,  the 
farther  the  point  B  is  taken  from  E  the  nearer  the  point 
F  will  approach  the  mirror.  Accordingly,  the  parts 
of  the  wave-front  which  fall  upon  MR  farthest  from  E 
will  be  brought  to  a  focus  nearest  to  the  mirror.  This 
defect  in  the  concave,  spherical  mirror  is  known  as 
Spherical  Aberration. 

Does  the  convex,  spherical  mirror  also  have  spherical 
aberration  ? 

Real  and  Virtual  Images  in  Concave  Mirrors. — In 
the  case  of  the  spherical  wave-front  reflected  from  the 
concave  mirror  in  Fig.  102,  it  will  be  seen  that  the 
virtual  image  of  5  is  back  of  the  mirror  much  farther 
than  5  is  in  front.  We  have  seen  that  a  plane  wave- 


352  PHYSICS 

front  after  reflection  from  t  a  concave  mirror  does  not 
appear  to  come  from  a  point  back  of  the  mirror  at  all, 
but  that  it  contracts  to  a  point  in  front  of  the  mirror. 
The  focus  of  the  plane  wave-front  may  accordingly  be 
regarded  as  a  real  image  of  the  source  of  light,  in  dis- 
tinction from  a  virtual  image  which  seems  to  exist 
back  of  the  mirror. 

Referring  again  to  Fig.  103,  it  will  be  seen  that  if  F 
be  taken  as  the  source  of  light,  the  reflected  rays  from 
the  mirror  will  be  parallel;  or,  in  other  words,  if  a 
spherical  wave  have  its  source  at  F,  it  will  become  a 
plane  wave  by  reflection  from  the  mirror. 

If  C,  the  center  of  curvature  of  the  mirror,  be  taken 
as  the  source  of  light,  the  wave-front  will  be  of  the 
same  curvature  as  the  mirror,  it  will  strike  all  parts  of 
the  mirror  surface  at  the  same  time,  and  will  be 
reflected  without  changing  its  curvature.  It  will,  how- 
ever, be  concave  after  reflection,  and  will  have  its  focus 
at  the  same  distance  as  C  from  the  mirror. 

A  spherical  wave  from  a  point  farther  from  the 
mirror  than  C  will  be  less  convex  at  the  mirror  than  a 
wave  from  C,  and  will  accordingly  be  brought  to  a 
focus  at  a  point  nearer  the  mirror  than  C,  or  between 
C  and  F.  Any  source  of  light  at  a  finite  distance 
greater  than  the  radius  of  curvature  in  front  of  a  con- 
cave, spherical  mirror  will  accordingly  have  a  real 
image  in  front  of  the  mirror  at  a  distance  greater  than 
the  focal  length  of  the  mirror. 

Fig.  104  represents  a  spherical  wave-front  WF  from 
S  reflected  from  the  concave  mirror  MR,  whose  center 
of  curvature  is  at  C.  On  the  assumption  that  the 
reflected  wave-front  is  spherical  (which  is  only  approxi- 
mately true),  it  will  have  its  center  at  S' .  It  will  be 


OPTICS  AND  RADIATION  353 

seen  that  S'  lies  farther  from  the  mirror  than  Fl ,  which 
represents  the  principal  focus  of  the  mirror. 

Accordingly,   any  source  of  light  on    the  principal 
axis  of  the  mirror  outside  the  center  of  curvature  will 

W\ 
\ 


FIG.  104. 

have  a  focus  between  the  center  of  curvature  and  the 
principal  focus  of  the  mirror. 

State  the  corresponding  law  for  a  source  of  light  between 
the  center  of  curvature  and  the  principal  focus. 

Conjugate  Foci. — The  points  S.  and  S'  are  called 
Conjugate  Foci,  since  if  either  of  them  is  taken  as  a 
source  of  light,  the  other  becomes  the  focus.,  A  source 
of  light  between  the  principal  focus  and  the  mirror  will 
seem  to  have  a  conjugate  focus  back  of  the  mirror,  but 
in  this  case  the  focus  is  virtual  and  not  real. 

Since  the  conjugate  focus  of  a  source  of  light  may  be 
regarded  as  the  image  of  that  source,  we  should  have 
both  real  and  virtual  images  formed  by  reflection  from 
a  concave  mirror.  We  have  already  seen  the  image 


354  PHYSICS 

of  the  Sun  formed  by  reflection  from  a  concave  mirror. 
We  will  now  try  to  project  real  images  of  other  objects 
in  the  same  way. 

Experiments  with  Concave  Mirror. 

LABORATORY  EXERCISE  125. — Stand  in  front  of  a  window 
with  a  concave  mirror,  and  try  to  project  an  image  of  the 
outside  landscape  or  the  clouds  upon  a  piece  of  opaque 
white  paper  held  between  the  mirror  and  the  window. 

Move  farther  back  and  try  to  project  an  image  of  the 
window  upon  the  paper  screen. 

Place  a  lighted  candle  or  lamp  in  a  darkened  room  and 
try  to  project  its  image  upon  the  screen.  What  peculiarity 
do  you  notice  in  the  images  formed  by  reflection  from  a  con- 
cave mirror  ? 

Fix  the  mirror,  and  find  a  position  for  the  candle  and 
screen  where  the  image  of  the  candle  will  be  as  distinct  and 
sharply  defined  as  possible,  then,  without  disturbing  the 
mirror,  change  positions  with  the  candle  and  screen.  Is  a 
clear  image  formed  in  the  new  position  ? 

What  names  do  you  give  to  the  positions  of  the  candle 
and  screen  ? 

In  which  case  is  the  image  larger  than  the  object  ?  Tell 
how  to  place  an  object  in  order  to  have  an  enlarged  image 
of  it  reflected  from  a  concave  mirror. 

Place  the  candle  so  that  you  can  see  its  virtual  image  in 
the  concave  mirror.  How  does  this  virtual  image  differ  in 
appearance  from  a  real  image  formed  by  the  mirror  ?  How 
does  it  differ  from  the  virtual  image  seen  by  reflection  in  a 
convex  mirror  ? 

Place  the  candle  in  a  position  in  front  of  the  mirror  where 
neither  a  real  nor  a  virtual  image  of  it  is  formed  by  reflection. 
What  is  the  shape  of  the  reflected  wave-front  in  this  case  ? 
How  can  you  measure  the  focal  length  of  the  mirror  from 
this  experiment  ?  Tell  where  to  place  the  lamp  of  a  loco- 
motive headlight  with  reference  to  its  reflector. 

Keeping  the  candle  and  screen  at  equal  distances  from 
the  mirror,  move  them  to  a  position  where  a  sharp  image 
will  be  formed  upon  the  screen,  and,  by  means  of  this  posi- 
tion, measure  the  radius  of  curvature  of  the  mirror.  What 
of  the  relative  size  of  the  object  and  image  in  this  position  ? 


OPTICS  AND  RADIATION 


355 


REFRACTION    OF    LIGHT 

Definition. — The  change  in  the  direction  or  the 
shape  of  a  wave-front  in  passing  from  one  medium  into 
another  is  called  Refraction. 

Refraction  at  Plane  Surface. 

LABORATORY  EXERCISE  126. — Place  a  glass  cube  with  faces 
two  or  three  inches  square  upon  an  ink  line  drawn  upon  a 
piece  of  paper  so  that  part  of  the  line  only  is  covered  by  the 
glass.  Look  downward  through  the  cube  at  the  ink  line. 
Does  the  part  seen  through  the  glass  seem  nearer  to  or  farther 
from  the  eye  than  the  parf  seen  through  the  air  only  ? 

In  the  experiments  on  reflection  we  saw  that  the  effect  of 
making  a  wave-front  more  convex  was  to  make  its  apparent 
source  seem  nearer  to  an  observer  than  its  real  source,  and 
vice  versa.  In  the  experiment  with  the  glass  cube,  is  the 
wave-front  of  light  apparently  made  more  or  less  convex 
on  emerging  from  glass  into  air  ? 


FIG.  105. 

In  Fig.  105  is  shown  the  change  in  shape  of  a  wave-front 
from  Sl  in  passing  from  one  medium  into  another  in  which 
its  velocity  is  increased  one  half.  The  effect  of  this  increased 
velocity  is  to  make  the  wave-front  more  convex  in  the  new 
medium,  and  to  change  the  apparent  position  of  the  source 
of  light  from  S^  to  Sz. 

Is  the  velocity  of  light  greater  or  less  in  glass  than  in 
air  ? 

Place  a  coin  in  a  tea-cup  or  other  vessel,  and  standing  so 


356  PHYSICS 

that  the  coin  is  just  hidden  from  view  by  the  edge  of  the 
vessel,  pour  water  into  the  vessel.  Does  the  coin  appear  to 
rise  into  view  ?  Is  the  wave-front  of  light  made  more  or 
less  convex  by  passing  from  water  into  air  ?  Is  the  velocity 
of  light  in  air  greater  or  less  than  in  water  ? 

Draw  the  projection  of  a  spherical  wave-front  passing  into 
a  plane-faced  medium  in  which  its  velocity  is  decreased  one 
half. 

To  an  observer  immersed  in  water  would  an  object  in  the 
air  seem  nearer  or  more  distant  than  the  real  object  ? 

In  Fig.  105  those  radii  of  the  refracted  wave-front  which 
are  oblique  to  the  surface  of  separation  of  the  two  substances 
seem  bent  at  this  surface.  Accordingly,  a  ray  of  light  is  said 
to  be  bent  in  passing  obliquely  from  one  medium  into 
another  in  which  its  velocity  is  changed.  When  the  velocity 
is  increased,  is  the  ray  bent  toward  or  from  a  perpendicular 
to  the  refracting  surface  at  the  point  of  emergence  ?  Draw 
the  ray  by  which  you  may  be  said  to  see  the  coin  in  the 
vessel  of  water. 

Hold  a  straight  rod,  as  a  lead-pencil,  about  half  under 
water  and  explain  the  apparent  bending  of  the  rod  at  the 
surface  of  the  water. 

To  a  person  immersed  in  the  water  how  would  the  rod 
seem  bent  at  the  surface  of  the  water  ? 

To  Find  the  Relative  Velocities  of  Light  in  Air 
and  Glass. 

LABORATORY  EXERCISE  127. — A  thick  glass  plate  with 
plane-parallel  sides  or  the  glass  cube  used  in  the  previous 
exercise  should  have  two  ink  lines  drawn  on  opposite  faces 
and  parallel  to  diagonally  opposite  edges.  Lay  the  glass 
plate  on  the  face  to  which  the  lines  are  drawn  perpendicular 
and,  with  a  pencil,  mark  the  outlines  of  the  plate  and  the 
positions  of  the  ink  lines,  as  in  Fig.  106,  in  which  S  and  R 
show  where  the  feet  of  the  ink  lines  meet  the  paper. 

Place  the  eye  on  a  level  with  the  glass,  and  looking 
through  it  from  R  to  S,  stick  a  pin  upright  in  the  paper,  as 
at  P,  where  it  will  appear  in  the  same  straight  line  with  R 
and  6".  Remove  the  glass  and  draw  the  lines  SR  and  PR, 
producing  PR  through  R  until  it  reaches  nearly  to  the  line 
A  C.  Draw  SN  perpendicular  to  the  two  opposite  faces, 
AB  and  CD. 


OPTICS  AND  RADIATION 


357 


If  we  now  consider  a  light  wave  from  the  source  S,  its 
apparent  source  as  seen  from  the  position  P  will  be  S' . 
Using  S  as  a  center,  draw  the  arc  RM.  This  will  represent 
the  form  which  the  wave-front  would  have  had  at  the  instant 


FIG.  106. 

of  reaching  R  if  its  velocity  in  air  had  been  the  same  as  in 
glass. 

With  S'  as  a  center,  draw  the  arc  RN.  This  will  repre- 
sent the  part  of  the  wave-front  in  air  at  the  instant  when  the 
part  in  glass  reaches  R,  It  must  be,  then,  that  the  wave- 
front  in  air  has  advanced  from  0  to  N  in  the  time  which 
would  have  been  required  for  it  to  advance  from  O  to  J^in 
glass.  Accordingly,  the  velocity  in  glass  is  to  the  velocity 
in  air  as  OM  is  to  ON. 

Measure  the  distances  OM  and  ON,  and  tell  how  the 
velocity  in  glass  compares  with  the  velocity  in  air. 

From  your  measurements,  what  is  the  velocity  of  light  in 
glass  in  miles  per  second  ?  In  meters  per  second  ? 

Refractive  Index. — The  velocity  of  light  in  air 
divided  by  its  velocity  in  any  given  substance  is  called 
the  Refractive  Index  of  that  substance.  Thus  the 
refractive  index  of  glass  is  ON  divided  by  OM. 

Calculate  the  refractive  index  of  glass. 

The  refractive  index  of  water  is  1.33;  what  is  the  velocity 
of  light  in  water  ? 


358 


PHYSICS 


Angle  of  Refraction. — If  in  Fig.  106  a  perpendic- 
ular be  drawn  through  CD  at  R,  the  angle  made  with 
this  perpendicular  by  SR  is  the  angle  of  incidence,  and 
the  angle  made  by  RP  and  the  perpendicular  is  the 
angle  of  refraction. 

It  will  be  seen  that  when  a  ray  of  light  passes 
obliquely  from  one  medium  into  another  in  which  its 
velocity  is  increased,  the  angle  of  refraction  is  greater 
than  the  angle  of  incidence.  If  P  be  taken  as  the 
source  of  light,  instead  of  5,  the  angle  .made  with  the 
perpendicular  by  SR  becomes  the  angle  of  refraction, 
which  in  this  case  is  less  than  the  angle  of  incidence. 

If  the  refractive  index  of  water  is  1.3  and  of  glass  is  1.6, 
how  will  a  ray  of  light  be  bent  in  passing  from  water  into 
glass  ? 

REFRACTION  AT  CURVED  SURFACES 

Refraction  of  Spherical  Surface. — In  Fig.  107  is 
shown  the  projection  of  a  spherical  wave-front,  WF, 
from  source  5  refracted  at  the 
spherical  surface  of  a  medium 
in  which  its  velocity  is  decreased 
one  third,  as  in  the  case,  of  a 
light  wave  entering  a  spherical 
glass  surface  from  the  air.  It 
will  be  seen  that  the  center  of 
the  wave-front  WF  first  enters 
the  refracting  surface  and  is 
retarded  more  than  the  edges, 
hence  the  section  of  the  wave- 
front  which  enters  the  refracting 
medium  is  rendered  less  convex 
by  refraction. 
Since  the  convexity  of  a  wave-front  is  decreased  by 


OPTICS  AND  RADIATION 


359 


refraction  upon  entering  a  convex,  spherical  surface  in 
which  its  velocity  is  decreased,  a  plane  wave-front  will 
be  rendered  concave  by  refraction  at  such  spherical 
surface. 

Lenses. — A  portion  of  a  transparent,  refracting  sub- 
stance bounded  by  two  surfaces  at  least  one  of  which 
is  spherical  is  called  a  Lens. 

The  six  principal  forms  of  lenses  are  shown  in  Fig. 
108.  Beginning  with  A,  they  are  named  as  follows: 

D  E  F 


FIG.  108. 

Double-convex,  Plano-convex,  Convex-meniscus, 
Double-concave,  Plano-concave,  and  Concave-menis- 
cus. 

The  three  first  named  are  also  called  converging 
lenses,  because  a  wave-front  is  made  less  convex  by 
passing  through  them.  This  follows  from  the  fact  that 
these  lenses  are  thicker  in  the  middle  than  at  the  edges, 
and  hence  the  central  part  of  the  wave-front  which 
passes  through  them  is  retarded  more  than  the  edges. 
The  concave  lenses,  on  the  other  hand,  retard  the 
center  of  the  wave-front  less  than  the  edges,  hence 
these  lenses  render  the  wave-front  more  convex  on  its 
passage  through  them  and  are  accordingly  called 
diverging  lenses.  Thus  the  rays  of  light  (which  are 
always  normals  to  the  wave-front)  are  made  to  con- 
verge by  passing  through  a  convex  lens,  and  to  diverge 
by  passing  through  a  concave  lens. 

Since  a  plane  wave-front  is  made  concave  by  passing 


360  PHYSICS 

through  a  convex  lens,  and  convex  by  passing  through 
a  concave  lens,  a  convex  lens  should  bring  a  plane 
wave-front  to  a  focus,  while  a  concave  lens  should 
make  it  appear  to  diverge  from  a  point  on  the  same  side 
of  the  lens  as  the  source  of  light. 

Refraction  by  a  Convex  Lens. 

LABORATORY  EXERCISE  128. — Hold  a  converging  lens*  in 
the  path  of  a  beam  of  sunlight  and  determine  the  point  at 
which  the  sunlight  is  brought  to  a  focus.  This  point  is 
called  the  principal  focus  of  the  lens.  Measure  the  focal 
length  of  the  lens. 

IMAGES  FORMED  BY  REFRACTION  IN  A  CONVEX  LENS 

Place  a  convex  lens  at  some  distance  from  a  window  and 
project  an  image  of  the  window  on  a  piece  of  white  paper 
or  ground  glass.  Can  you  project  an  image  of  the  outside 
landscape  ? 

Place  a  lighted  lamp  or  candle  in  a  dimly  lighted  room 
and  by  means  of  a  convex  lens  project  its  image  upon  a 
screen.  Find  the  position  for  the  lamp  and  screen  which 
gives  the  clearest  possible  image,  then  leaving  the  lens  in 
position,  change  places  with  the  lamp  and  screen.  Has  a 
convex  lens  conjugate  foci  ? 

Leaving  the  lamp  and  screen  in  position,  move  the  lens 
into  another  position  between  them  where  it  will  project  a 
clear  image  of  the  lamp  on  the  screen.  Explain.  What 
difference  do  you  observe  in  the  two  images  ? 

If  the  lighted  lamp  be  placed  at  the  principal  focus  of  the 
lens,  what  is  the  shape  of  the  refracted  wave-front  ?  Is  an 
image  formed  in  this  case  ? 

Can  you  place  the  lamp  in  a  position  where  its  image  will 
be  virtual  ?  Explain. 

Calling  £  in  Fig.  107  the  position  of  the  lighted  lamp, 
tell  how  it  is  placed  with  reference  to  the  principal  focus  of 
the  lens. 

Where  would  you  place  the  lamp  in  order  to  have  its  real 
image  as  large  as  possible  ? 

*  Convex  lenses  sold  as  reading  glasses  answer  well  for  this  experi- 
ment. One  of  about  4  inches  in  diameter  is  most  convenient. 


OPTICS  AND  RADIATION 


361 


Where,  in  order  to  have  its  virtual  image  as  large  as 
possible  ? 

In  what  respects  do  the  images  of  convex  lenses  resemble 
those  of  concave  mirrors  ? 

Refraction  by  Concave  Lenses. 

LABORATORY  EXERCISE  129. — Let  a  beam  of  sunlight  pass 
through  a  small  hole  in  a  screen  and  fall  upon  a  piece  of 
white  paper.  Note  the  size  of  the  spot  of  light  and  then 
place  a  concave  lens  *  in  the  path  of  the  beam  between  the 
screen  and  the  paper.  What  change  do  you  observe  in  the 
spot  of  light  on  the  paper  ?  Explain. 

Try  whether  you  can  project  an  image  of  the  lighted  lamp 
by  means  of  a  concave  lens.  Look  through  the  lens  at  the 
lamp.  Do  you  see  a  virtual  image  ?  If  so,  is  the  image 
nearer  to  or  farther  from  the  lens  than  the  lamp  ?  Explain. 

Draw  a  figure  showing  the  passage  of  a  spherical  wave- 
front  through  a  plano-concave  lens.  \ 

M 

TOTAL   REFLECTION 

Cause  of  Total  Reflection. — In  Fig.  109  is  shown 
the  projection  of  a  spherical  wave-front  from  the  source 
S  refracted  by  passing  into  a  medium  in  which  its 


velocity  is  increased  one  half.  It  will  be  seen  that 
while  the  secondary  wave-fronts  produced  by  the 
middle  part  of  the  incident  wave  combine  to  form  a 

*  A  large  spectacle  lens  answers  well  for  this  experiment. 


362  PHYSICS 

single  refracted  wave-front,  the  secondary  wave-fronts 
frdm  M1  and  M2  lie  wholly  without  the  main  wave-front 
at  the  points  of  emergence  from  the  refracting  surface. 
It  will  also  be  seen  that  the  secondary  wave-fronts 
from  points  on  AB  outside  of  M1M2  will  lie  outside 
those  from  Ml  and  Mr  It  follows  that  for  points  on 
the  refracting  surface  outside  the  circle  whose  diameter 
is  M1M2  the  secondary  wave-fronts  will  not  combine  to 
form  a  continuous  wave-front,  and  that  consequently 
no  wave-front  from  vS  will  emerge  except  within  this 
circle. 

Experiments  on  Total  Reflection. 

LABORATORY  EXERCISE  130. — Lay  a  coin  in  a  large,  shallow 
dinner  plate  near  the  side  farthest  from  you  and  pour  water 
over  it  until  the  plate  is  nearly  full.  Then  look  at  the  coin 
while  you  lower  your  eye  nearly  to  the  level  of  the  water 
surface.  If  the  plate  is  wide  enough,  the  coin  will  disappear 
from  view  before  it  is  hidden  by  the  side  of  the  plate. 

If  a  very  broad,  shallow  vessel  be  used,  a  row  of  coins 
may  be  placed  in  the  line  of  sight,  and  as  the  eye  is  lowered 
the  farthest  coins  will  disappear  first. 

This  experiment  shows  that  the  light  from  the  coin  can 
emerge  from  the  water  only  for  a  definite  distance  on  any 
side  of  the  coin. 

Fill  a  round-bottomed,  smooth  goblet  or  wine  glass  with 
water,  and  look  downward  through  the  water  and  the  sides 
of  the  vessel  at  objects  outside  the  vessel.  You  will  be  able 
to  see  readily  through  a  circular  area  near  the  bottom,  but 
not  through  the  sides  near  the  top. 

Since  in  the  experiment  with  the  coin  in  water  light  from 
the  coin  must  strike  the  whole  surface  of  water  in  the  plate, 
the  question  naturally  arises  as  to  what  becomes  of  the  light 
which  cannot  emerge  from  the  water  into  the  air.  To 
answer  this  question,  lay  the  glass  cube  used  in  former 
experiments  upon  an  ink  cross  marked  upon  white  paper. 
Looking  downward  through  the  glass  you  can  see  the  cross 
plainly.  Can  you  look  through  one  side  and  the  bottom 
and  see  the  cross  ? 


OPTICS  AND  RADIATION 


363 


Can  you  look  through  the  top  and  one  of  the  vertical  sides 
and  see  objects  outside  the  cube  ? 

Since  the  light  which  enters  the  bottom  of  the  cube  cannot 
pass  out  through  one  of  the  vertical  sides,  it  would  seem 
that  it  must  be  either  reflected  or  absorbed  by  the  side. 
Can  you,  by  looking  through  the  top,  see  evidence  that  the 
light  from  the  cross  is  reflected  from  the  sides  of  the  cube  ? 
Does  this  reflection  take  place  from  all  the  four  sides  ? 

Can  you  hold  the  cube  in  such  a  position  that  light  will 
pass  through  two  sides  at  right  angles  to  each  other  ? 

In  ordinary  reflection  a  part  of  the  light  passes  through 
the  reflecting  surface.  In  these  experiments,  since  none  of 
the  light  passes  through  the  reflecting  surface,  the  reflection 
is  said  to  be  Total. 

Can  total  reflection  take  place  when  light  enters  a  medium 
in  which  its  velocity  is  decreased  ? 

REFRACTION    BY  TRIANGULAR   PRISM 

Change  in  Direction  of  Wave  by  Triangular  Prism. 

— In  Fig.  no  is  shown  the  change  in  direction  of  a 
light  wave  in  passing  through  a  triangular  prism  whose 
refractive  index  is  i .  5 .  It  will  be  seen  that  on  enter- 


FIG.  no. 

ing  the  prism  the  wave-front  is  changed  from  arc  ab 
with  its  center  at  5  to  arc  ac  with  its  center  at  S' '. 
The  wave-front  accordingly  advances  through  the 
prism  as  if  its  source  were  Sf,  but  upon  emerging  again 


364  PHYSICS 

into  the  air  its  convexity  will  be  increased,  and  it  will 
advance  as  if  its  source  were  S" .  To  an  observer  at 
P  the  source  5  will  accordingly  appear  to  be  at  S" ', 
and  the  broken  line  PQRS  will  represent  the  path  of  a 
ray  of  light  from  5  to  P. 

To  Trace  the  Path  of  a  Ray  through  a  Triangular 

Prism. 

LABORATORY  EXERCISE  131. — Draw  an  ink  line  on  one  side 
of  a  triangular  glass  prism  parallel  to  the  edges  of  the  prism. 
Set  the  prism  on  end  on  a  sheet  of  paper  and  draw  its  outline 
with  a  pencil,  as  ABC  in  Fig.  no.  Mark  the  foot  of  the 
ink  line  on  the  paper,  as  R.  Stick  a  pin  upright  to  one  side 
of  the  prism,  as  at  S,  and  looking  through  the  prism  from 
the  other  side,  stick  a  pin  P  where  it  seems  to  be  in  a 
straight  line  with  R  and  S.  Stick  a  third  pin  at  Q,  where 
the  line  PRS  leaves  the  prism.  Remove  the  prism  and 
draw  PQ,  QR,  and  RS. 

The  virtual  image  of  the  pin  which  you  see  on  looking 
through  the  prism  will  then  appear  in  the  line  PQ  produced. 

DISPERSION   OF   LIGHT 

Dispersion  hy  Triangular  Prism. 

LABORATORY  EXERCISE  132. — Cut  a  slit  about  one  milli- 
meter wide  in  a  piece  of  thin  sheet  metal  or  smooth  card- 
board,* mount  it  upright  on  a  board,  cover  it  with  red  glass 
and  set  it  in  front  of  a  window  and  reflect  a  beam  of  sunlight 
upon  it  with  a  mirror  or  a  heliostat.  Set  a  prism  parallel  to 
the  slit  in  the  path  of  the  beam  of  red  light,  and  place  a 
ground -glass  or  paper  screen  at  a  distance  of  about  a  meter 
from  the  prism  to  receive  the  colored  image  of  the  slit. 
Notice  the  displacement  of  the  red  image  of  the  slit  due  to 
its  passage  through  the  prism.  Mark  on  the  screen  the 
boundaries  of  this  image. 

Without  moving  the  prism  or  screen,  remove  the  red  glass 
from  the  slit  and  replace  it  by  a  piece  of  blue  glass,  and 
mark  again  the  boundaries  of  the  image. 

Which  is  more  refracted,  red  light  or  blue  light  ? 

*  Such  a  slit  is  most  easily  cut  with  a  sharp  chisel. 


OPTICS  AND  RADIATION  365 

Remove  the  colored  glass  and  note  the  image  made  by  the 
uncolored  sunlight.  Are  the  red  and  blue  images  in  their 
former  positions  ?  What  other  colors  can  you  distinguish, 
and  what  are  their  orders  of  refraction  ? 

Which  colored  light  has  been  most  retarded  by  its  passage 
through  the  prism  ?  Which  color  has  been  least  retarded  ? 

Was  the  light  which  passed  through  the  red  glass  colored 
by  the  glass,  or  does  the  sunlight  contain  red  light  ?  What 
became  of  the  other  colors  when  the  red  glass  was  inter- 
posed ? 

The  Spectrum. — The  colored  band  of  light  produced 
by  the  overlapping  images  of  the  slit  is  called  a  Spec- 
trum. If  the  slit  be  made  very  narrow,  so  that  each 
colored  image  is  very  narrow,  the  images  will  not 
overlap  so  much,  and  each  part  of  the  spectrum  is  said 
to  consist  of  a  pure  color.  Seven  of  these  so-called 
primary  colors  are  easily  distinguished  and  are  named 
in  their  order,  beginning  with  the  color  most  refracted, 
Violet,  Blue,  Peacock,  Green,  Yellow,  Orange,  Red. 
No  sharp  dividing  line  can  be  drawn  between  adjacent 
primary  colors,  as  in  every  case  the  color  changes 
gradually  from  one  to  the  other. 

Recombination  of  Spectrum. 

LABORATORY  EXERCISE  133. — With  the  apparatus  arranged 
as  before,  place  a  glass  cylinder  or  round  bottle  about  two 
inches  in  diameter  filled  with  water  in  the  path  of  the  spec- 
trum where  it  is  about  a  centimeter  wide.  This  cylinder 
will  act  as  a  converging  lens  to  refract  the  diverging  light 
toward  a  central  line.  Hold  a  piece  of  white  paper  back  of 
the  cylinder  to  receive  the  light,  and  adjust  the  position  of 
the  paper  until  the  line  of  light  upon  it  is  as  narrow  as 
possible. 

Does  the  re-combination  of  the  spectrum  produce  ordinary 
sunlight  ? 

Newton  was  the  first  to  prove  that  the  sunlight  is  made 
up  of  a  combination  of  lights  of  different  color,  and  that 
these  colors  are  refracted  by  different  amounts  in  passing 
through  a  prism. 


366 


PHYSICS 


FIG.  in. 


Complementary  Colors. 

LABORATORY  EXERCISE  134. — A  glass  cylinder  such  as  was 
used  in  the  preceding  experiment  has 
black  paper,  cut  as  in  Fig.  in,  pasted 
upon  one  of  its  sides.  Place  this  cylinder 
filled  with  water  in  the  path  of  the  diverg- 
-g  ing  spectrum  with  the  paper  on  the  side 
toward  the  prism.  Adjust  it  parallel  to 
the  prism,  and  allow  the  spectrum  to  fall 
upon  it  half  above  and  half  below  the 
line  AB.  The  spectrum  should  be  about 
a  centimeter  in  width  at  the  cylinder. 

It  will  be  seen  that  precisely  the  same 
part  of  the  spectrum  is  allowed  to  pass  through  the  slit  above 
AB  that  is  cut  out  by  the  strip  below  AB.  Place  a  paper 
back  of  the  cylinder  where  the  colors  are  combined  upon  it 
as  in  the  former  experiment.  You  will  now  have  differently 
colored  lines  above  and  below  AB.  The  two  colors  obtained 
at  one  time  are  such  that  when  combined  they  will  produce 
ordinary  sunlight.  They  are  accordingly  called  Complemen- 
tary Colors.  They  are  not  the  primary  colors  of  the 
spectrum,  but  each  is  made  up  of  the  combined  colors  of  a 
part  of  the  spectrum,  while  the  other  is  made  up  of  the 
combined  colors  of  the  rest  of  the  spectrum. 
Name  three  pairs  of  complementary  colors. 
Color  of  Bodies. — Since  we  can  see  non-luminous 
bodies  only  by  the  light  which  they  reflect  to  the  eye, 
all  the  possible  colors  of  bodies  must  exist  in  ordinary 
sunlight.  In  general,  bodies  do  not  reflect  equally 
well  all  the  colors  of  the  sunlight  which  falls  upon 
them.  Usually  some  of  the  light  enters  the  bodies 
and  is  absorbed,  while  another  part  is  reflected.  In 
this  case,  the  color  of  the  body  is  the  color  resulting 
from  the  combination  of  the  primary  colors  which  it 
reflects,  and  is  complementary  to  the  colors  which  are 
absorbed. 

Sometimes    bodies    absorb    one    part    of  the    light, 
transmit  another  part,  and  reflect  a  third  part.      Such 


OPTICS  AND  RADIATION  367 

bodies  seem  of  different  color  when  seen  by  transmitted 
light  than  when  seen  by  reflected  light.  A  little 
ordinary  red  ink  in  a  glass  of  water  usually  shows  a 
different  color  when  we  look  through  it  at  the  light 
than  when  seen  by  reflected  light. 

Color  is  accordingly  a  property  of  light.  Most 
bodies  seem  colored  on  account  of  their  selective 
absorption  of  light.  Most  vegetable  bodies  contain 
chlorophyll,  which  is  a  great  absorber  of  red  light, 
hence  the  light  which  we  receive  by  reflection  from 
these  bodies  is  the  complementary  color  of  the  red 
light  absorbed. 

Dispersion  in  Lenses. 

LABORATORY  EXERCISE  135 — Cut  a  square  hole  in  a  piece 
of  thin  metal  or  cardboard,  cover  it  with  red  glass,  and  light 
it  strongly  by  means  of  reflected  sunlight  or  a  lamp  placed 
near  it. 

By  means  of  a  convex  lens  placed  on  the  side  opposite  the 
light,  project  a  sharp  image  of  the  square  hole  on  a  screen 
of  white  paper.  When  the  screen  is  placed  in  position  to 
give  the  sharpest  possible  image,  replace  the  red  glass  by  a 
piece  of  blue  glass.  Must  you  move  the  screen  nearer  to 
or  farther  from  the  lens  in  order  to  project  a  sharp  image  by 
blue  light  ? 

Is  the  focal  length  of  the  lens  for  red  light  greater  or  less 
than  for  blue  light  ? 

Remove  the  colored  glass  and  see  if  you  can  project  an 
image  of  the  hole  where  it  will  be  surrounded  by  a  red  band. 
Where  it  will  be  surrounded  by  a  blue  band. 

What  proofs  have  you  of  dispersion  in  lenses  ? 

Chromatic  Aberration. — The  defect  in  lenses  which 
you  have  just  observed  is  called  Chromatic  Aberration. 
Since  refraction  is  always  accompanied  by  dispersion, 
it  is  impossible  to  construct  a  simple  lens  of  a  single 
substance  which  will  not  show  chromatic  aberration. 

It  has  been  found,  however,  that  dispersion  is  not 


368 


PHYSICS 


proportional  to  refraction.  Some  prisms  produce  a 
much  broader  spectrum  for  the  same  amount  of  devia- 
tion of  the  refracted  beam  than  do  others.  Thus  if 
prisms  made  of  crown  glass  and  flint  glass  produce 
exactly  the  same  amount  of  deviation  for  red  light,  the 
flint-glass  prism  will  produce  a  greater  deviation  of  the 
blue  light.  If  these  prisms  be  placed  together  with 
their  bases  in  opposite  directions,  a  beam  of  red  light 
will  not  be  refracted  in  passing  through  both ;  but  if  a 
beam  of  sunlight  be  passed  through  them,  a  spectrum 
will  be  produced. 

On  the  other  hand,  if  prisms  of  crown  and  flint  glass 
be  so  made  that  they  will  produce  the  same  dispersion, 
the  crown-glass  prism  will  produce  a  greater  deviation 
than  the  flint-glass  prism,  and  they  can  be  made  to 
refract  a  beam  of  light  without  producing  noticeable 
dispersion. 

Achromatic  Lenses.  —  Lenses  are  corrected  for 
chromatic  aberration  by  using  a  concave  lens  of  flint 

glass  with  a  convex  lens  of 
crown  glass.  Such  a  lens  has 
a  much  greater  focal  length 
than  the  crown-glass  lens 
alone,  since  the  flint-glass  lens 
is  a  diverging  lens;  but  by 
opposing  the  dispersion  of  one 
lens  to  that  of  the  other  the 
red  and  blue  light  may  be  brought  to  the  same  focus. 
A  lens  corrected  in  this  way  is  known  as  an  Achro- 
matic lens. 

In  Fig.  112  are  shown  some  of  the  common  forms 
of  achromatic  lenses.  In  every  case  the  convex  lens 
is  of  crown  glass,  and  the  concave  lens  of  flint  glass. 


FIG.  112. 


OPTICS  AND  RADIATION 


369 


INTERFERENCE   OF   LIGHT 
INTERFERENCE   BY   REFLECTION 

Newton's  Rings. 

LABORATORY  EXERCISE  136. — Take  two  pieces  of  plate 
glass  with  plane,  polished  faces,*  and  press  them  together 
with  a  slight  rotary  motion  until  they  cling  together  by 
cohesion.  (If  the  glass  faces  are  not  sufficiently  plane  to 
make  a  good  contact,  breathe  upon  them  and  let  moisture 
condense  over  them  and  form  a  surface.)  Place  the  two 
glass  plates  in  a  position  where  they  will  reflect  light  to  the 
eye  from  their  surfaces  of  contact.  If  they  are  sufficiently 
close  together,  there  will  be  seen  colored  bands  of  light 
reflected  from  their  surfaces  of  contact.  Fig.  1 1 3  is  from  a 


FIG.  113. 

photograph   of  such  a  pair  of  plates  showing  the  colored 
bands. 

Increase  the  pressure  upon  one  edge  of  the  plates  by 
means  of  the  fingers  or  a  clamp,  and  notice  that  the  colored 

*  The  glass  slides  used  for  microscopic  work  usually  answer  well  for 
this  experiment. 


370  PHYSICS 

bands  seem   to  surround   the  place  of  greatest  pressure  in 
more  or  less  regular  forms. 

Change  the  pressure,  and  notice  that  the  bands  move  as 
if  their  position  depended  upon  the  distance  between  the 
plates. 

Lay  the  plates  upon  a  dark  surface  in  a  dimly  lighted  part 
of  the  room  and  illuminate  them  by  yellow  light  made  by 
heating  common  salt  on  a  piece  of  asbestos  or  wire  in  the 
non-luminous  Bunsen  flame  or  in  an  alcohol  flame.  Observe 
that  in  this  case  the  bands  are  yellow  and  black  only,  and 
that  many  more  of  them  can  be  seen  than  in  sunlight. 

In  one  form  of  the  apparatus  frequently  used  for  this 
experiment  one  of  the  plates  is  plane  and  the  other  is  a 
convex,  spherical  surface  of  large  radius.  With  this  form  of 
apparatus  the  plates  touch  in  only  one  place,  and  the  bands 
are  seen  to  surround  this  place  of  contact  in  more  or  less 
symmetrical  rings.  This  is  the  form  in  which  the  apparatus 
was  first  used  by  Newton,  and  the  colored  bands  were 
accordingly  known  as  Newton's  Rings. 

Notice  that  at  the  place  of  closest  contact  of  the  plates  a 
dark  spot  is  formed,  and  that  this  is  surrounded  by  alternate 
yellow  and  black  bands.  As  the  plates  become  farther  and 
farther  apart,  these  bands  become  closer  together.  Appa- 
rently, wherever  the  two  surfaces  are  at  a  certain  distance  or 
some  multiple  of  this  distance  apart,  the  light  reflected  from 
one  surface  quenches  the  light  reflected  from  the  other  sur- 
face, while  at  intermediate  distances  apart  the  light  from  both 
surfaces  combines  to  increase  the  intensity.  The  bands  are 
accordingly  called  Interference  Bands. 
^vComparison  with  Sound  Interference. — In  the  ex- 
periments on  Sound,  page  219,  you  saw  that  a  sounding 
tuning  fork  when  moved  toward  and  from  a  reflecting 
wall  had  its  sound  weakened  or  strengthened  by  the 
sound  waves  reflected  from  the  wall,  according  as  its 
distance  to  the  wall  and  back  was  an  uneven  or  an  even 
number  of  half  wave-lengths. 

If  we  suppose  a  row  of  tuning  forks  of  the  same  pitch 
standing  at  an  angle  to  the  reflecting  wall,  as  Fl,  F2, 
F^j  etc.,  in  Fig.  114,  where  AB  represents  the  line  of 


OPTICS  AND  RADIATION  37* 

the  wall,  some  of  these  forks  will  have  the  intensity  of 
their  sound  increased  and  some  diminished  by  the 
reflection  from  the  wall.  A  listener  walking  along  the 
line  of  forks  might  notice  this  variation  in  intensity, 
that  is,  might  recognize  interference  bands  of  sound. 

Suppose,  again,  a  row  of  forks  of  different  pitch  to 
be  sounded  together  and  all  moved  toward  and  from  the 
wall,  keeping  the  line  parallel  to  the  wall  all  the  time. 

"    '* 


FIG.  114. 

In  this  case,  destructive  interference  would  occur  at 
different  distances  from  the  wall  for  different  forks,  and 
the  resultant  sound  of  the  forks  would  depend  upon  the 
distance  of  their  line  from  the  wall.  In  any  position 
of  the  forks  some  of  them  would  have  their  sound 
weakened  and  some  strengthened,  and  the  resultant 
sound  would  be  the  sum  of  the  original  sounds  of  all 
the  forks,  less  the  sounds  cut  out  by  interference.  We 
would  accordingly  have  sounds  of  different  pitch  pro- 
duced by  interference,  just  as  we  have  lights  of  different 
colors  produced  by  interference  in  the  Newton's  Rings 
apparatus. 

Theory  of  Interference.  —  Our  explanation  of  the 
formation  of  the  interference  bands  of  light  is  accord- 
ingly as  follows: 

Let  A  and  B,  Fig.  115,  represent  the  two  glass 
plates,  and  WF  a  wave-front  of  light  from  the  source  S. 
Let  sl  and  s2  be  points  upon  the  inner  reflecting  sur- 


372 


PHYSICS 


faces  of  the  two  plates  which  are  reached  in  the  same 
time  by  the  wave-fronts  from  5.  sl  and  s2  will  accord- 
ingly be  the  centers  of  two  reflected  waves  starting  at 
the  same  time.  These  waves  will  meet  in  the  same 
phase  at  some  point,  as  a,  on  the  surface  of  the  plate 
Ay  and  the  point  a  will  be  illuminated  by  both  waves. 
On  either  side  of  a  one  wave-front  will  be  behind  the 
other,  the  wave-front  from  s^  being  behind  on  one  side 

8 


FIG.  115. 

and  the  wave-front  from  s2  on  the  other  side.  At 
equal  distances  on  each  side  of  a,  as  at  b  and  c,  the 
distance  between  these  wave-fronts  will  be  half  a  wave 
length  of  light,  and  where  these  points  emerge  from 
the  glass  plate  the  successive  waves  will  interfere 
destructively  with  each  other.  The  point  a  will  accord- 
ingly'represent  the  position  of  a  light  band,  and  the 
points  b  and  c  positions  of  dark  bands. 

Fig.  1 1 6  is  made  from  a  photograph  of  ripples  made 
in  mercury  by  two  pointed  wires  attached  to  the  same 
prong  of  a  tuning  fork  so  that  they  will  both  enter  and 
leave  the  mercury  at  the  same  time  as  the  fork  vibrates 
up  and  down.  The  ripples  from  both  vibrating  points 
accordingly  start  at  the  same  time  and  spread  out  in 


OPTICS  AND  RADIATION  373 

the  form  of  circular  waves  just  as  a  light  disturbance 
spreads  out  from  its  center  in  spherical  waves.  Along 
the  lines  where  the  crest  of  one  ripple  meets  the  crest  of 
another,  a  row  of  high  ripples  is  seen,  while  along  those 
lines  where  the  crest*  of  one  ripple  meets  the  trough 
of  another  the  surface  of  the  mercury  is  not  thrown 
into  ripples  at  all.  There  are  accordingly  interference 


FIG.  116. 

bands  radiating  over  the  surface  which  is  covered  by 
the  two  systems  of  ripples,  just  as  interference  bands 
of  light  would  radiate  from  sl  and  s2  in  Fig.  115. 

If  light  of  many  different  wave-lengths  be  used  with 
the  Newton's  Rings  apparatus,  then  some  particular 
wave  length  will  interfere  for  each  distance  of  separa- 
tion of  the  reflected  wave-fronts  from  the  two  plates, 
while  other  wave-lengths  may  combine  to  increase  the 
intensity  of  their  illumination  at  these  same  distances 
of  separation.  This  being  true,  complete  interference 
bands  can  be  produced  only  when  all  the  light  waves 

*  The  crests  of  the  ripples  are  shown  by  the  light  bands  in  the  photo- 
graph. 


374  PHYSICS 

reflected  are  nearly  of  the  same  length,  and  the  waves 
of  the  yellow  sodium  light  made  by  heating  salt  in  the 
flame  must  be  all  of  nearly  the  same  wave-length. 

The  sunlight,  on  the  contrary,  must  be  made  up  of 
many  different  wave-lengths.  When  the  colored  bands 
are  formed  by  the  interference  of  sunlight,  some  of 
these  wave-lengths  are  cut  out  at  every  distance  of 
separation  of  the  plates,  and  the  color  of  the  resultant 
band  at  any  point  on  the  plate  must  be  the  resultant  of 
all  the  colors  which  are  not  cut  out  at  that  point. 

Estimation  of  Wave-length  by  Interference. 

LABORATORY  EXERCISE  137. — Place  the  interference  plates 
in  the  sunlight  so  that  the  colored  bands  can  be  seen,  and 
then  hold  a  piece  of  red  glass  so  that  only  the  light  which 
has  passed  through  this  glass  can  fall  upon  the  plates  and 
observe  the  distance  between  the  interference  bands.  Repeat, 
allowing  only  blue  light  to  fall  upon  the  plates.  In  which 
case  are  the  interference  bands  closer  together  ? 

Would  the  interference  bands  of  long  waves  or  of  short 
waves  be  closer  together  ? 

Which  apparently  has  the  greater  wave-length,  red  light 
or  blue  light  ? 

If  all  light  waves  travel  with  the  same  velocity,  which 
color,  red  or  blue,  is  due  to  the  more  rapid  vibrations  ? 

Periodic  Character  of  Light  Waves. — In  our  earlier 
discussion  of  light  waves  nothing  was  said  about  their 
periodic  character,  and  our  only  assumption  was  that 
these  waves  are  spherical.  We  have  now  seen  reason 
to  believe  that  these  spherical  waves  follow  each  other 
periodically  and  very  close  together.  The  term  wave- 
length is  applied,  as  in  sound,  to  the  distance  between 
the  similar  phases  of  two  successive  waves.  Thus,  in 
the  circular  ripples  on  the  mercury  surface  a  wave- 
length is  the  distance  measured  along  the  radius  of  the 
circle  from  the  crest  of  one  ripple  to  the  crest  of  the 


OPTICS  AND  RADIATION  375 

next  one,  or  from  the  trough  of  one  ripple  to  the  trough 
of  the  next,  or  from  any  phase  of  one  to  the  corre- 
sponding phase  of  the  next.  The  wave-length  has  no 
relation  to  the  wave-front.  The  wave-front  of  the  sun- 
light at  the  earth  we  have  already  seen  is  the  surface 
of  a  sphere  of  about  93,000,000  miles  radius.  The 
mean  wave-length  of  light  is  about  one  fifty-thousandth 
of  an  inch.  That  is,  these  spherical  waves  follow  each 
other  about  a  fifty- thousandth  of  an  inch  apart. 

INTERFERENCE   BY   DIFFRACTION 

Diffraction  by  Narrow  Obstacle. 

LABORATORY  EXERCISE  138. — There  are  many  ways  of 
dividing  a  wave-front  of  light  into  two  parts  each  of  which 
becomes  a  new  source  of  spherical  waves  which  may  interfere 
with  each  other,  as  do  the  ripples  from  the  two  centers  of 
disturbance  on  the  mercury  surface.  One  of  these  methods 
is  given  in  the  following  exercise. 

Place  in  front  of  a  window  a  screen  in  which  has  been  cut 
a  vertical  slit  about  one  millimeter  wide,  with  smooth  edges, 
and  reflect  direct  sunlight  through  the  slit  by  means  of  a 
mirror  or  heliostat.  At  a  distance  of  about  a  meter  from 
the  slit  place  a  vertical  wire,  as  a  small  knitting-needle  or  a 
hat-pin,  so  that  it  shall  be  in  the  path  of  the  beam  of  light 
which  passes  through  the  slit  and  parallel  to  its  edges.  At 
a  distance  of  one  or  two  meters  from  the  wire  place  a  screen 
of  ground  glass  or  greased  paper  where  the  light  from  the 
slit  and  the  shadow  cast  by  the  wire  may  fall  upon  it.  If 
the  shadow  of  the  wire  is  in  the  middle  of  the  image  of  the 
slit  and  is  exactly  parallel  to  its  edges,  this  shadow  will  be 
seen  to  be  composed  of  vertical  dark  and  light  or  colored 
bands,  beginning  with  a  light  band  in  the  center  of  the 
shadow  and  having  at  least  two  very  distinct  dark  bands, 
one  on  each  side  of  the  light  band.  These  bands  are  called 
interior  interference  fringes.  If  your  adjustment  is  good, 
you  will  be  able  to  also  see  interference  fringes  outside  the 
edges  of  the  shadow,  called  exterior  fringes. 

Since  the  light  which  passes  the  edges  of  the  wire  seems 
to  be  bent,  or  diffracted,  so  as  to  enter  the  shadow  of  the 


376  PHYSICS 

wire,  the  interference  bands  seen  in  the  shadow  are  said  to 
be  produced  by  diffraction. 

If  we  regard  the  interference  bands  as  produced  by  spheri- 
cal light  waves  having  their  sources  in  points  on  the  opposite 
edges  of  the  wire,  the  method  of  their  production  may  be 
seen  from  Fig,  117. 


6 


\ 


FIG.  117. 

Thus,  if  A  and  B  represent  the  points  upon  the  edges  of 
the  wire  at  which  two  spherical  waves  originate  at  the  same 
time,  these  two  waves  will  meet  in  the  same  phase  at  a,  and 
a  vertical  line  through  a  will  be  illuminated  by  both  waves. 
At  points  b  and  c  one  of  these  waves  may  be  just  half  a  wave 
length  behind  the  other,  as  in  the  case  of  the  reflected  wave- 
fronts  from  the  glass  plates  in  Fig.  115.  In  this  event,  the 
two  wave-fronts  will  interfere  destructively  at  b  and  c,  and 
the  shadow  of  the  wire  will  contain  vertical  dark  bands 
through  these  points.  Outside  of  b  and  c,  say  at  points  d 
and  e,  the  successive  wave-fronts  from  A  and  B  will  be  an 
entire  wave-length  behind  each  other,  and  points  d  and  e 
will  accordingly  be  illuminated  by  both  sets  of  waves. 

If  waves  of  more  than  one  wave-length  are  sent  off  from 
A  and  B,  the  interference  fringes  will  occur  at  different 
points  for  waves  of  different  length;  hence  only  the  first  pair 
of  dark  bands  will  appear  nearly  black,  while  the  others  will 
be  colored  by  waves  not  cut  out  by  interference  at  that  dis- 
tance from  a. 

Measurement  of  Wave-length  by  Diffraction. — A 

rough  measurement  of  the  wave-length  of  light  may  be 
made  by  the  following  method: 


OPTICS  AND  RADIATION  377 

Let  the  circle  in  Fig.  118  represent  a  cross-section 
of  the  wire  used  in  the  diffraction  experiment,  AB 
representing  a  diameter  and  A'B'  the  width  of  the 
shadow  of  the  wire  on  the  screen.  Let  a  be  the  central 
light  band  in  this  shadow,  and  b  the  position  of  the 
first  interior  dark  band  on  one  side.  Regarding  A  and 
B  as  the  sources  of  the  light  waves  which  interfere  at 
b,  the  distance  Bb  must  be  greater  than  Ab  by  half  a 
wave-length  of  light, 


FIG.  118. 


Letting  A.  =  the  wave-length  of  light,  and  calling 
the  radius  of  the  wire  r,  the  distance  of  the  wire  from 
the  screen  =  Ca  =  d,  and  the  distance  ab  =  c,  we  have 
the  following  equations  : 

Ab*  —  d*  +  (r  —  cf     and     Bb*  —  d*  +  (r  +  cf. 

Hence  B&  —  At?  =  ^cr. 

Also,  5?  -  Ab*  =  (Bb  +  Ab)(Bb  -  Ab). 

Bb  -\-  Ab  may,  for  the  purpose  of  the  demonstration, 

be  taken   as  equal  to   2d,  and  Bb  —  Ab  —  -,   hence 
Bt?  -  A&  =  d\  =  4cr,  and  A  = 


378  PHYSICS 

To  Measure  the  Wave-length  of  Sunlight. 

LABORATORY  EXERCISE  139. — Place  the  screen  as  far  from 
the  wire  as  will  allow  the  interference  fringes  to  be  distinctly 
seen,  and  with  the  vernier  calipers  measure  the  distance  from 
the  outer  edge  of  one  of  the  central  dark  bands  to  the  inner 
edge  of  the  other.  This  distance  is  2c. 

With  the  same  calipers  measure  the  diameter  of  the  wire, 
which  is  2r.  Measure  d  with  the  meter  rule  or  tape,  and 
calculate  A. 

The  Diffraction  Grating. — A  number  of  very  close, 
equally  spaced,  parallel  obstacles  placed  in  the  path  of 
a  beam  of  light,  as  was  the  wire  in  the  diffraction 
experiment,  is  called  a  Diffraction  Grating.  Diffraction 
gratings  are  often  made  by  ruling  fine,  parallel 
scratches  on  a  glass  plate  by  means  of  a  diamond 
point.*  These  scratches  disperse  the  light  which  falls 
upon  them  and  thus  serve  as  obstacles  to  the  passage 
of  light,  while  the  clear  spaces  between  them  serve  as 
the  sources  of  the  secondary  waves  considered  in  the 
interference  experiments. 

Thus,  in  Fig.  119,  if  Siy  S2,  53,  etc.,  represent  the 
sources  of  the  secondary  waves  and  the  spaces  between 
them  represent  the  obstacles,  we  have  a  large  number 
of  waves  following  each  other  at  equal  distances  and 
interfering  at  the  same  places  as  would  the  waves  from 
a  single  pair  of  luminous  points.  The  result  is  to 
greatly  increase  the  intensity  of  illumination  of  the 
light  bands. 

Thus  at  M  the  pairs  of  waves  starting  from  equal 
distances  on  each  side  of  53  will  always  meet  in  the 
same  phase  and  strengthen  each  other.  If  m  be  the 

*  Gratings  suitable  for  the  following  experiments  can  be  made  by 
ruling  parallel  lines  on  a  microscope  slide  by  use  of  a  dividing  engine. 
Gratings  having  200  and  400  lines  to  the  centimeter  will  answer  per- 
fectly for  these  experiments,  though  finer  gratings  can  be  used  as  well. 


OPTICS  AND  RADIATION  379 

position  of  the  first  dark  band,  it  is  plain  that  the  suc- 
cessive waves  will  here  follow  each  other  at  distances 
of  a  half  wave-length  apart.  At  n,  which  is  the  posi- 
tion of  a  light  band,  the  wave-fronts  will  be  a  whole 
wave-length  apart.  Accordingly,  if  light  of  a  single 

\\\ 


M 


FIG.  119. 

wave-length  be  passed  through  the  grating  and  a  screen 
placed  at  a  distance  in  front  of  it,  a  series  of  light  and 
dark  bands  will  appear  upon  the  screen. 

If,  instead  of  allowing  the  light  to  pass  through  the 
grating  and  fall  upon  a  screen,  we  hold  the  grating 
before  the  eye  and  look  at  a  narrow  source  of  light, 
as  the  edge  of  a  lamp  flame  or  an  illuminated  slit,  we 
shall  see  the  successive  light  bands  arranged  as  they 
would  be  upon  a  screen  as  far  from  the  grating  as  the 
grating  is  now  held  from  the  source  of  light. 

The  Grating  Spectrum.  —  If  light  of  different  wave- 
lengths fall  upon  the  grating,  the  points  where  the 
bright  bands  will  appear,  as  at  ny  will  be  different  for 
different  wave-lengths.  It  is  plain  that  since  n  repre- 
sents the  point  where  the  successive  wave-fronts  are  a 
single  wave-length  apart,  the  shorter  the  wave-length 
of  the  light  used  the  nearer  n  will  lie  to  M.  The 
grating  will  accordingly  sort  out  lights  of  different 
wave-lengths  and  arrange  them  in  parallel  bands  in 


380 


PHYSICS 


the  order  of  their  wave-length.  Such  a  sorting  will 
produce  a  spectrum  similar  to  the  prism  spectrum. 

To  observe  this  spectrum,  stand  at  a  distance  of 
several  meters  from  a  lighted  lamp  and  look  at  the 
edge  of  the  lamp  flame  through  a  diffraction  grating 
held  near  the  eye. 

Place  a  red  glass  in  front  of  the  flame  or  hold  it 
against  the  grating,  and  look  as  before.  Notice  the 
distance  between  the  red  images  of  the  flame,  and  then 
look  at  it  from  the  same  position  through  a  grating 
having  the  lines  ruled  twice  as  close  together.  What 
difference  do  you  observe  in  the  distance  between  the 
images  ? 

Measurement  of  Wave-length  by  Diffraction  Grat- 
ing.— In  Fig.  120,  let  5X  and  S2  represent  two  of  the 
transparent  spaces  in  a  diffraction  grating,  let  M  repre- 
sent the  central  light  band  on  a  screen,  and  n  the  first 
light  band  on  one  side  of  the  center.  Then  if  S2c  be 
drawn  perpendicular  to  S^,  S^  will  equal  A,  one  wave- 
length of  light. 


M 


FIG.  120. 

Let  the  distance  5X52  =  d.  Then,  since  5X52  is  very 
small  as  compared  with  the  distance  S1M1  S}M  and 
S2M  may  be  regarded  as  parallel  and  the  angle 


OPTICS  AND  RADIATION  381 

may  be  considered  a  right  angle.  We  then  have  the 
similar  triangles  S^cS2  and  S^Mn,  and  accordingly 

-j  =  -„—,  or  by  Trigonometry,  calling  the  angle  MSji 

(t  ^  .71 

the  angle  Q,  A  —  a?  sin  Q. 

To  Measure  the  Wave-length  of  Sodium  Light. 

LABORATORY  EXERCISE  140. — Place  a  sodium  flame  close 
to  and  back  of  a  narrow,  vertical  slit  in  a  darkened  corner, 
place  a  meter  scale  horizontal  just  above  or  below  the  slit, 
and  place  a  diffraction  grating  at  a  distance  of  five  or  six 
meters  so  that  you  can  look  through  it  at  the  lighted  slit. 
Notice  the  series  of  bright  bands  on  each  side  of  the  central 
slit,  and  locate  on  the  scale  the  farthest  one  from  the  center 
on  each  side  that  you  can  see  distinctly.  Divide  the  dis- 
tance between  these  two  bright  bands  by  the  number  of  dark 
spaces  between  them,  and  the  quotient  will  give  you  the 
distance  Mn  more  accurately  than  you  can  measure  it 
between  a  single  pair  of  bands. 

Measure  carefully  the  distance  between  the  grating  and 
the  scale  for  Sji,  and  taking  the  distance  d  as  marked  on  the 
grating,  calculate  A  for  the  sodium  light. 

Repeat,  using  another  grating  with  a  different  ruling. 

Careful  measurements  by  this  method  will  give  the  value 
of  A  within  one  per  cent  of  the  true  value,  and  measurements 
giving  a  value  differing  more  than  two  or  three  per  cent  from 
the  true  value  should  be  repeated. 

The  wave-length  of  yellow  sodium  light  is  .000896  milli- 
meter; if  the  velocity  of  light  be  taken  as  300,000,000 
meters  a  second,  what  number  of  vibrations  a  second  is 
required  to  produce  the  sodium  light  ? 

What  is  the  wave-length  of  sodium  light  in  glass  having  a 
refractive  index  of  1.5  ? 

RECTILINEAR   PROPAGATION 

Rectilinear  Propagation  Due  to  Interference. — The 

earlier  notion  of  light  propagation  was  that  light 
traveled  in  straight  lines.  We  shall  now  see  how  this 
notion  arose. 

Referring  again  to  Fig.  1 19,  note  what  would  be  the 


382  PHYSICS 

effect  of  introducing  other  sources  of  light  midway 
between  Slt  S2 ,  etc.  We  see  at  once  that  the  wave- 
fronts  at  n  would  be  only  half  as  far  apart,  and  that  a 
dark  band  would  be  at  n  instead  of  a  light  band.  The 
effect  would  accordingly  be  to  cut  out  half  of  the  bright 
images  of  the  flame  formed  by  the  grating. 

Was  this  what  you  observed  in  looking  through  the 
two  gratings  at  the  lamp  flame  ?  Place  a  meter  stick 
horizontal  just  back  of  the  flame  and  note  again  the 
apparent  position  of  the  red  images  of  the  flame  as 
seen  against  the  scale.  Are  just  half  of  the  images 
cut  out  by  making  the  light  sources  just  half  as  far 
apart  ? 

Carry  this  reasoning  farther,  and  you  will  see  that 
if  the  light  sources  were  infinitely  close  together,  the 
first  bright  image  on  one  side  of  M  would  be  at  an 
infinite  distance  from  M,  or,  in  other  words,  if  light 
passes  through  an  opening  in  which  there  are  no 
obstacles,  it  produces  only  one  spot  of  light  on  the 
screen,  and  this  spot  is  the  one,  represented  in  the 
figure  at  Mt  which  will  be  reached  by  the  light  from 
the  center  of  the  opening  in  the  least  time.  All  of  the 
light  falling  upon  the  screen  at  a  distance  from  M  will 
be  blotted  out  by  interference  of  other  light  waves  fall- 
ing upon  the  same  spot.  The  rectilinear  propagation 
of  light  is  accordingly  seen  to  be  an  interference 
phenomenon. 

We  have  seen  that  the  longer  the  light  wave,  the  farther 
from  M  will  be  its  first  dark  interference  band,  and  accord- 
ingly the  wider  will  be  the  spot  of  light  on  the  screen 
about  M.  Will  the  spot  of  light  formed  on  a  screen  by 
passing  sunlight  through  a  narrow  slit  be  wider  when  the  slit 
is  covered  with  blue  glass  or  with  red  glass  ?  Try  the 
experiment  with  the  slit  at  a  distance  of  several  meters  from 


OPTICS  AND  RADIATION  383 

the  screen,  one  half  of  the  slit  being  covered  with  blue  and 
the  other  half  with  red  glass,  or,  better,  holding  the  blue  and 
red  glasses  with  their  edges  together  against  the  side  of  the 
screen  turned  toward  the  light. 

Why  are  sound  shadows  not  so  definite  as  light  shadows  ? 

DOUBLE    REFRACTION   AND    POLARIZATION 

Double  Refraction  in  Iceland  Spar. — Certain  trans- 
parent crystals,  as  Iceland  Spar,  have  the  property  of 
separating  a  beam  of  light  which  passes  through  them 
in  certain  directions  into  two  beams  which  diverge  after 
leaving  the  crystal.  If  you  hold  such  a  crystal  before 
the  eye  and  look  through  it  at  a  pin-hole  in  a  piece  of 
opaque  paper  held  against  the  side  of  the  crystal,  you 
will  apparently  see  two  pin-holes,  and  they  will  seem 
at  different  distances  apart  according  to  the  direction 
in  which  you  look  through  the  crystal. 

Since  the  change  in  the  direction  of  light  in  passing 
through  the  crystal  is  due  to  refraction,  the  two  beams 
must  be  differently  refracted,  and  the  crystal  is  said  to 
possess  the  property  of  double  refraction. 

One  of  these  beams  in  Iceland  Spar  has  the  same 
refractive  index  in  any  direction  through  the  crystal, 
as  in  isotropic  bodies,  so  it  is  called  the  ordinary  beam. 
The  other  beam  has  a  different  refractive  index  in 
different  directions  through  the  crystal,  and  is  called 
the  extraordinary  beam.  This  means,  of  course,  that 
the  light  of  the  ordinary  beam  has  the  same  velocity  in 
all  directions  through  the  crystal,  while  the  extraor- 
dinary beam  travels  with  different  velocities  in  differ- 
ent directions.  Hence,  if  a  source  of  light  were  placed 
in  the  center  of  a  crystal  of  Iceland  Spar,  there  would 
be  two  kinds  of  light  waves  sent  off  from  it.  One  of 
these  kinds  would  consist  of  spherical  waves,  as  in 


384  PHYSICS 

isotropic  bodies,  and  the  other  would  be  made  up  of 
waves  having  different  velocities  of  propagation  in 
different  directions.  In  the  case  of  Iceland  Spar  the 
extraordinary  waves  are  of  the  shape  of  oblate  spheroids, 
having  their  shortest  diameter  the  same  as  that  of  the 
corresponding  spherical  waves.  Accordingly,  there  is 
one  direction  through  the  crystal  in  which  both  sets  of 
waves  travel  with  the  same  velocity,  and  hence  a  beam 
of  light  passing  through  the  crystal  in  that  direction 
will  not  be  doubly  refracted.  In  all  other  directions 
the  extraordinary  waves  travel  with  a  greater  velocity 
than  the  ordinary  waves. 

Double  Refraction  in  Tourmaline. — The  ordinary 
and  extraordinary  waves  produced  by  double  refraction 
must  differ  in  some  important  property  to  account  for 
the  difference  in  their  method  of  propagation.  In 
order  to  study  their  properties  separately  it  is  desirable 
to  have  some  method  of  isolating  them.  For  this 
purpose  the  Tourmaline  Tongs  are  frequently  used. 

Tourmaline  is,  like  Iceland  Spar,  a  doubly  refracting 
crystal,  but  it  possesses  the  additional  property  of 
absorbing  the  ordinary  waves,  so  that  a  section  of  the 
crystal  of  a  thickness  of  a  little  more  than  a  millimeter 
will  absorb  the  ordinary  waves  completely  and  allow 
only  the  extraordinary  waves  to  pass  through  it.  The 
tourmaline  tongs  consist  of  two  sections  of  tourmaline 
crystal  cut  of  such  a  thickness  as  to  absorb  the  ordinary 
beam,  and  mounted  parallel  to  each  other  in  a  wire 
handle. 

Polarization  by  Double  Refraction. 

LABORATORY  EXERCISE  141. — Hold  the  tourmaline  tongs 
in  front  of  the  eye  and  look  through  both  crystals  at  a  lighted 
window.  Turn  one  of  the  crystals  in  its  ring  until  the 
greatest  possible  amount  of  light  passes  through  both.  This 


OPTICS  AND   RADIATION  385 

light  is  colored  because  tourmaline  is  a  colored  crystal  and 
transmits  only  light  of  certain  wave-lengths. 

Holding  one  crystal  fixed,  rotate  the  other  until  no  light 
passes  through  the  two.  You  will  find  by  careful  observa- 
tion that  you  must  rotate  the  crystal  through  just  ninety 
degrees  to  accomplish  this.  Notice  that  the  light  will  pass 
through  either  crystal  alone  when  rotated  in  any  direction. 

We  have  now  seen  that  when  light  has  been  passed 
through  a  tourmaline  crystal  its  properties  have  been  changed 
so  that  another  crystal  may  or  may  not  transmit  it  accord- 
ing as  the  crystal  is  rotated  around  the  beam  of  light  as  an 
axis.  Since  the  light  which  passes  through  tourmaline  is  the 
extraordinary  beam  produced  by  double  refraction,  we  find 
that  this  beam  differs  from  ordinary  sunlight  in  other 
respects  besides  having  a  differently  shaped  wave-front. 
Since  tourmaline  transmits  the  extraordinary  beam  and 
absorbs  the  ordinary  it  must  be  that  when  the  light  passes 
through  both  crystals  it  is  an  extraordinary  beam  in  both. 
When  one  crystal  has  been  rotated  through  ninety  degrees, 
the  beam  of  light  which  before  entered  it  as  an  extraordinary 
beam  apparently  enters  it  as  an  ordinary  beam,  and  is 
absorbed  by  the  crystal.  By  looking  through  one  of  the 
tourmaline  crystals  at  the  two  images  of  the  pin-hole  seen 
through  the  Iceland  Spar,  you  will  see  that  by  rotating  the 
tourmaline  you  can  cause  it  to  cut  off  the  light  from  either 
the  ordinary  or  the  extraordinary  beam  of  the  Iceland  Spar. 
It  would  accordingly  seem  that  an  extraordinary  beam  in  a 
crystal  can  be  changed  to  an  ordinary  beam  by  rotating  it 
around  the  line  of  propagation  through  ninety  degrees,  and 
vice  versa. 

Light  Waves  Due  to  Transverse  Vibration. — We 

can  explain  this  phenomenon  only  by  supposing  light 
to  be  due  to  waves  of  transverse  vibration,  instead  of 
waves  of  compression  and  rarefaction  as  in  sound. 
Thus,  in  ordinary  sunlight  there  are  waves  vibrating  in 
all  directions  at  right  angles  to  the  line  of  propagation 
of  the  light.  In  a  doubly  refracting  crystal,  all  of 
these  waves  except  those  vibrating  in  two  directions  at 
right  angles  to  each  other  are  apparently  quenched. 


386  PHYSICS 

Then  the  waves  which  vibrate  in  one  direction  travel 
faster  in  certain  directions  than  those  vibrating  at  right 
angles  to  them.  In  tourmaline  one  set  of  these  waves 
is  absorbed  before  they  have  penetrated  far  into  the 
crystal,  while  the  others  pass  through  and  emerge  with 
their  vibrations  all  perpendicular  to  one  plane.  Such 
light  is  said  to  be  Plane-polarized. 

Polarization  of  Hertzian  Waves. — An  analogous 
phenomenon  has  been  observed  in  the  electric  waves 
sent  off  from  the  spark  discharge  of  an  electric  machine 
or  Leyden  jar.  When  these  waves  are  passed  through 
a  thick  wooden  plank  they  are  found  to  be  plane- 
polarized,  just  as  light  waves  are  polarized  in  passing 
through  a  section  of  tourmaline.  The  vibrations  of  the 
electric  waves  in  the  plank  can  apparently  take  place 
only  lengthwise  or  crosswise  of  the  grain  of  the  wood. 
When  electric  waves  enter  the  plank  each  one  is 
apparently  separated  into  two  waves,  one  of  which  has 
all  its  vibrations  parallel  to  the  grain  of  the  wood,  while 
in  the  other  the  vibrations  are  all  perpendicular  to  the 
grain  of  the  wood.  One  of  these  waves  is  propagated 
with  a  greater  velocity  than  the  other,  and  one  is 
absorbed  more  rapidly  than  the  other.  Accordingly, 
after  the  waves  have  passed  through  a  sufficient  thick- 
ness of  the  wood  only  one  set  emerges.  If  another 
piece  of  plank  with  its  grain  parallel  to  the  first  be 
interposed  in  the  path  of  the  wave,  it  will  pass  through 
this  plank  also.  If  the  second  plank  have  its  grain 
crosswise  to  the  first,  it  will  absorb  the  waves  which 
have  passed  through  the  first  plank.  Electric  waves  are 
accordingly  plane-polarized  by  passing  them  through 
a  wooden  block  perpendicular  to  the  grain  of  the  wood. 

If  the  waves  are  passed  endwise  through  the  block, 


OPTICS  AND  RADIATION  387 

so  that  their  vibrations  must  all  be  perpendicular  to  the 
wood  fibers,  they  are  not  doubly  refracted.  In  the 
same  way,  there  is  one  direction  through  Iceland  spar 
and  tourmaline  crystals  in  which  double  refraction  does 
not  take  place.  This  direction  is  called  the  Optic  Axis 
of  the  crystals.  Sections  of  crystal  prepared  for  pro- 
ducing double  refraction  are  cut  parallel  to  the  optic 
axis,  just  as  boards  are  sawed  parallel  to  the  fibers  of 
the  wood. 

Polarization  accordingly  teaches  us  one  more  fact 
about  the  nature  of  light  waves  and  electric  waves, 
viz.,  that  in  these  waves  the  vibrations  are  transverse 
to  the  direction  of  propagation  as  in  waves  on  the  sur- 
face of  water,  and  not  parallel  to  this  direction,  as  in 
sound  waves.  Thus,  when  a  spherical  wave  is  set  up 
in  the  Luminiferous  Ether,  the  vibrations  of  the  Ether 
particles  are  everywhere  perpendicular  to  the  radii  of 
the  sphere,  and  accordingly  parallel  to  the  wave- 
front. 

Polarization  by  Reflection. 

LABORATORY  EXERCISE  142. — Lay  a  piece  of  glass  upon 
the  table,  preferably  upon  a  piece  of  dark  cloth  or  paper, 
and  stand  a  lighted  candle  near  it.  Then,  standing  at  a 
distance  of  a  few  feet  from  it,  look  at  the  reflection  of  the 
candle  flame  in  the  glass  while  you  rotate  one  of  the.  tourma- 
line crystals  before  your  eye.  Is  the  reflected  light  partly 
polarized  ?  If  not,  change  your  position  until  you  see  the 
image  of  the  flame  partly  quenched  by  the  rotation  of  the 
tourmaline.  Observe  that  the  amount  of  polarization 
depends  upon  the  angle  at  which  the  light  falls  upon  the 
glass.  Estimate  as  nearly  as  you  can  the  angle  at  which  the 
light  is  most  completely  polarized. 

Theory  of  Polarization  by  Reflection. — When  a 
beam  of  ordinary  light  falls  upon  a  reflecting  surface 
the  Ether  vibrations  are  supposed  to  be  in  any  or  all 


3  88  PHYSICS 

directions  perpendicular  to  the  path  of  the  beam. 
Some  of  them  are  accordingly  parallel  to  the  reflecting 
surface,  while  others  at  right  angles  to  these  are 
approximately  perpendicular  to  it.  It  is  believed  that 
one  of  these  sets  is  more  readily  refleoted  than  the 
other,  while  the  other  set  more  easily  penetrates  the 
glass.  The  reflected  beam  accordingly  has  more 
vibrations  in  one  of  these  directions  than  did  the  inci- 
dent beam,  while  the  light  which  penetrates  the  glass 
has  a  corresponding  excess  of  light  polarized  in  the 
other  direction. 

It  is  generally  believed  that  the  light  polarized  by 
reflection  has  its  vibrations  parallel  to  the  glass  surface, 
while  the  light  which  passes  through  the  glass  has  its 
vibrations  perpendicular  to  these;  but  the  actual  direc- 
tion of  vibration  cannot  be  definitely  ascertained. 

If  a  number  of  glass  plates  be  bound  together  making 
several  reflecting  surfaces  parallel  to  each  other,  a  much 
larger  proportion  of  the  incident  light  may  be  reflected 
and  polarized  by  them  than  by  a  single  plate.  The 
thin  glass  strips  sold  for  microscopic  cover  glasses  are 
well  adapted  to  this  purpose.  If  you  have  such  a 
polarizer,  mount  it  in  a  vertical  position  and  allow  the 
light  of  a  lamp  or  candle  to  fall  upon  it  at  the  angle  of 
most  complete  polarization  and  observe  with  the  tour- 
maline that  the  light  transmitted  through  the  polarizer 
is  polarized  at  right  angles  to  the  reflected  light. 
Notice  that  when  the  light  is  made  to  pass  through  a 
red  glass  before  falling  upon  the  polarizer  it  is  more 
completely  polarized  than  when  ordinary  uncolored 
light  is  used.  This  is  due  to  the  fact  that  the  angle  of 
reflection  for  complete  polarization  is  different  for 
different  wave-lengths,  and  it  is  only  when  monochro- 


OPTICS  AND  RADIATION  389 

matic  light  is  used  that  complete  polarization  can  be 
obtained  by  reflection. 

THE    NATURE   OF   LIGHT 

Visible  and  Invisible  Radiation.  —  In  our  first 
experiments  on  Light  we  found  it  to  be  a  form  of  radia- 
tion propagated  in  spherical  waves  in  an  all-pervading 
medium  called  the  Luminiferous  Ether.  By  means  of 
interference  phenomena  we  were  able  to  show  that 
these  waves  follow  each  other  periodically  at  very  small 
distances  apart.  From  the  phenomena  of  polarization 
we  have  learned  that  they  are  waves  of  transverse 
vibration.  We  have  also  learned  of  other  forms  of 
radiation  which  are  not  visible  to  our  eyes,  as  the 
radiation  from  a  heated  body  which  is  not  luminous, 
and  the  radiation  from  an  electric  spark  or  from  an 
electric  discharge  through  a  vacuum  tube.  All  of 
these  forms  of  invisible  radiation  except  the  X-Radia- 
tion  of  Roentgen,  the  velocity  of  which  has  not  been 
measured,  are  known  to  be  propagated  with  the  velocity 
of  light,  and  are  capable  of  reflection,  refraction,  inter- 
ference, and  polarization,  as  are  ordinary  light  waves. 
They  ,are  accordingly  waves  of  transverse  vibration  in 
the  Luminiferous  Ether,  and  are  different  from  light 
waves  only  in  having  a  greater  wave-length. 

Relation  of  Visibility  to  Wave-length  of  Radiation. 
—The  longest  waves  of  visible  radiation  are  less  than 
.0008  millimeter  in  length,  but  if  the  spectrum  of  the 
Sun  be  thrown  upon  a  screen  and  its  heating  effects  be 
studied  by  means  of  a  delicate  thermometer,  they  will 
be  found  to  extend  far  beyond  the  red  end  of  the  spec- 
trum. The  invisible  radiation  at  this  end  of  the 
spectrum  is  made  up  of  longer  waves  than  the  visible 


390  PHYSICS 

spectrum,  and  is  known  as  the  Infra-Red  spectrum. 
By  means  of  delicate  apparatus  the  infra-red  spectrum 
has  been  detected  to  a  wave-length  of  about  .025 
millimeter. 

If  a  photographic  plate  be  exposed  to  the  solar 
spectrum  and  suitably  developed,  the  plate  will  be 
found  blackened  by  invisible  radiation  beyond  the 
violet  end  of  the  visible  spectrum.  The  shorter  waves 
at  this  end  of  the  spectrum  are  known  as  Ultra- Violet. 
While  the  shortest  wave  of  visible  radiation  is  about 
.0004  millimeter  in  length,  the  ultra-violet  spectrum 
has  been  photographed  to  a  wave-length  of  about 
.0001  millimeter. 

The  visible  radiation  is  accordingly  but  a  small  part 
of  the  total  radiation  of  the  sun.  Thus,  if  a  grating 
spectrum  of  the  Sun  be  thrown  upon  a  screen  at  such 
a  distance  that  the  visible  spectrum  is  four  inches  long, 
the  known  ultra-violet  spectrum  will  likewise  be  four 
inches  long  and  the  known  infra-red  spectrum  will  be 
twelve  feet  long. 

In  terms  of  the  musical  notation  used  in  describing 
sound  vibrations,  the  total  known  spectrum  of  the  Sun 
consists  of  about  eight  octaves.  Of  these,  two  belrfng 
to  the  ultra-violet  spectrum,  one  belongs  to  the  visible 
spectrum,  and  five  belong  to  the  infra-red  spectrum. 

The  shortest  electric  waves  which  have  yet  been 
studied  are  about  six  millimeters  long,  and  are  accord- 
ingly about  eight  octaves  below  the  longest  known 
infra-red  waves. 

Unknown  Nature  of  Roentgen  Radiation.  —  All 
attempts  at  measuring  the  wave-length  of  the  Roentgen 
radiation  have  failed.  This  radiation  has  not  yet  been 
regularly  reflected,  refracted,  nor  polarized.  It  is 


OPTICS  AND  RADIATION  391 

accordingly  a  mere  matter  of  speculation  as  to  the  place 
which  these  waves  would  occupy  in  the  spectrum  could 
they  be  dispersed  by  a  prism  or  a  grating.  Since  they 
resemble  ultra-violet  radiation  in  some  of  their  proper- 
ties, they  are  supposed  by  some  physicists  to  be  very 
short  waves  beyond  the  ultra-violet  end  of  the  spectrum. 

The  Becquerel  Radiation. — Besides  the  Roentgen 
radiation  there  are  several  other  known  kinds  of  invisi- 
ble radiation  which  are  capable  of  producing  fluorescent 
or  photographic  effects.  One  of  the  best  known  of 
these  is  the  form  of  radiation  given  off  by  the  metal 
Uranium  and  some  of  its  compounds  as  well  as  by  a 
number  of  other  so-called  "  Radioactive  "  substances, 
and  called  after  its  discoverer  the  Becquerel  Radiation. 
It  is  similar  in  its  properties  to  the  Roentgen  radiation 
and  its  wave-length  is  unknown. 

Electro-magnetic  Origin  of  all  Radiation. — Max- 
well's theory  of  the  electromagnetic  origin  of  all  radia- 
tion is  now  generally  believed.  According  to  this 
theory  light  waves  are  caused  by  vibration  of  electric- 
ally charged  atoms  or  parts  of  atoms,  and  are  trans- 
mitted by  the  electric  elasticity  of  the  Luminiferous 
Ether.  It  is  not  known  that  the  Ether  has  any  other 
kind  of  elasticity,  or  that  it  can  be  set  in  vibration  by 
anything  but  electric  charges. 

PROPERTIES   OF   THE   ETHER 

Properties  Inferred  from  Nature  of  Radiation. — It 
is  principally  from  the  phenomena  of  radiation  that  we 
learn  of  the  properties  of  the  Luminiferous  Ether.  We 
know  that  it  is  a  medium  which  exists  throughout  the 
entire  known  physical  universe,  for  our  only  knowledge 
of  the  heavenly  bodies  is  obtained  through  radiation. 


392  PHYSICS 

It  also  permeates  all  known  transparent  bodies,  since 
these  transmit  radiation  with  a  greater  velocity  than 
would  be  possible  from  the  properties  of  the  bodies 
themselves.  If  light  were  transmitted  by  glass  instead 
of  by  the  Ether  in  glass,  its  velocity  would  depend 
upon  the  elasticity  and  the  density  of  glass,  as  does  the 
velocity  of  a  sound  wave;  but  the  velocity  of  light 
through  glass  is  about  40,000  times  the  velocity  of 
sound  in  the  same  medium. 

We  know  also  that  the  Ether  is  capable  of  trans- 
mitting transverse  vibrations,  hence  it  must  have 
properties  analogous  to  those  of  a  solid  body.  The 
most  common  conception  of  the  Ether  is  that  it  is  a 
jelly-like  substance  having  an  elasticity  much  greater 
in  proportion  to  its  density  than  any  known  material 
body,  and  allowing  the  atoms  of  material  bodies  to  pass 
through  it  without  appreciable  resistance.  It  seems, 
however,  to  exert  a  pressure  upon  the  atoms  of  bodies 
as  it  also  does  upon  bodies  having  an  electric  charge, 
and  it  is  generally  supposed  that  cohesion  and  gravita- 
tion are  due  to  Ether  pressures  upon  the  atoms  of 
material  bodies.  This  being  the  case,  the  Ether  itself 
would  not  be  subject  to  gravitation  and  hence  would 
not  have  weight. 

SPECTRUM   ANALYSIS 

Emission  Spectra. — We  have  seen  in  our  experi- 
ments on  dispersion  that  different  sources  of  light  give 
different  spectra.  Thus,  while  a  lamp  flame  gives  a 
spectrum  showing  nearly  the  same  color  as  the  Sun's 
spectrum,  the  sodium  flame  gives  a  spectrum  having 
no  colors  in  it  but  yellow.  When  the  sodium  flame  is 
observed  through  a  prism  or  a  grating  only  a  yellow 


OPTICS  AND  RADIATION  393 

image  of  the  slit  is  seen.  If  the  slit  be  narrow,  this 
becomes  merely  a  yellow  line ;  but  if  the  slit  be  very 
narrow  and  the  image  be  magnified  by  a  lens,  it  will 
be  seen  to  consist  of  two  yellow  lines  very  close 
together.  These  lines  are  the  two  images  of  the  very 
narrow  slit  made  by  two  kinds  of  yellow  light  of  nearly 
the  same  wave-length. 

Characteristic  Spectra  of  the  Elements.— If  the 
flame  be  colored  with  lithium  instead  of  sodium,  a  red 
line  is  seen  instead  of  a  yellow  one.  If  potassium  be 
heated  in  the  flame,  its  spectrum  will  show  a  red  line 
and  a  blue  one.  Thus  each  particular  element  gives 
its  own  characteristic  spectrum  when  its  vapor  is  suffi- 
ciently heated. 

Continuous  Spectra. — The  spectrum  of  a  hot  solid 
or  liquid  is  always  a  continuous  spectrum,  that  is,  it  is 
not  made  up  of  separate  images  of  the  slit,  but  of  over- 
lapping images. 

A  heated  gas  is  apparently  capable  of  setting  up 
light  waves  of  certain  wave-lengths  only,  while  a  heated 
solid  or  liquid  may  set  up  light  waves  of  all  wave- 
lengths. The  spectrum  of  a  lamp  flame  is  accordingly 
not  a  gas  spectrum,  but  the  spectrum  of  a  heated  solid. 
That  is,  the  light  given  off  by  the  flame  is  the  light 
from  the  solid  particles  of  carbon  which  are.  heated  to 
incandescence  before  they  combine  with  the  oxygen  of 
the  air.  When  the  combustion  becomes  complete,  the 
flame  becomes  non-luminous,  as  in  the  alcohol  flame 
or  the  non-luminous  flame  of  the  Bunsen  burner. 

Radiation  Due  to  Atomic  Vibrations. — Since  each 
element  has  its  own  gas  spectrum,  it  seems  that  the 
vibrations  which  produce  the  light  waves  must  be  the 
vibrations  of  the  atoms  in  the  molecule,  and  not  the 


394  PHYSICS 

vibrations  of  the  molecules  themselves.  We  have 
already  seen  reasons  for  believing  that  the  molecules 
of  a  gas  are  making  all  kinds  of  irregular  vibrations, 
striking  each  other  and  rebounding  in  every  direction 
and  with  all  kinds  of  velocities.  Such  vibrations  would 
not  have  the  periodic  character  necessary  for  producing 
light  waves  of  definite  wave-length.  The  atoms  in 
each  particular  kind  of  molecule  seem,  however,  to 
have  definite  periods  of  vibration.  Thus  the  atoms  in 
the  sodium  molecule  seem  to  make  about  500,000,- 
000,000,000  vibrations  in  a  second.  The  atoms  of 
lithium  vibrate  more  slowly,  while  the  atoms  of  potas- 
sium have  two  periods  of  vibration,  one  much  slower 
and  one  much  faster  than  the  sodium  atoms. * 

It  is  only  when  the  mean  free  path  of  the  molecules 
is  great  enough  to  allow  the  atoms  to  vibrate  in  their 
proper  periods  between  the  molecular  impacts  that  an 
element  can  give  its  characteristic  spectrum.  In  solids 
and  liquids  the  molecules  seem  to  be  so  close  together 
that  their  impacts  are  constantly  jarring  the  atoms  out 
of  their  normal  periods  of  vibration,  and  hence  waves 
of  many  different  wave-lengths  are  being  given  off  by 
different  atoms  at  the  same  time. 

Use  of  Spectrum  Analysis. — Spectrum  Analysis  is 
the  method  of  determining  the  composition  of  bodies  in 
the  gaseous  state  by  means  of  the  spectra  which  they 
emit. 

The  Spectroscope. — The  instrument  most  used  for 
studying  the  spectra  of  different  substances  is  known  as 
the  Spectroscope.  It  is  shown  in  diagram  in  Fig.  121. 
It  consists  essentially  of  a  tube  carrying  an  adjustable 

*  Recent  investigations  make  it  seem  probable  that  light  waves  are 
produced  by  the  vibrations  of  the  electrons  mentioned  on  pages  165  and 
278,  rather  than  by  the  chemical  atoms. 


OPTICS  AND  RADIATION  395 

slit,  called  the  collimator  tube,  as  shown  at  A,  a  prism 
or  grating,  as  at  B,  and  an  observing  telescope  for 
viewing  the  spectrum,  as  at  C.  The  collimator  tube 
regularly  has  a  lens  at  the  end  nearest  the  prism  to 
render  the  rays  from  the  slit  parallel  before  they  fall 
upon  the  prism,  and  the  telescope  is  focused  so  as  to 
give  an  image  of  the  slit  as  seen  through  the  prism  by 
monochromatic  light.  The  spectroscope  is  also  fre- 


FlG     121. 

quently  provided  with  another  tube,  as  at  D,  carrying 
a  scale  photographed  on  glass  which  can  be  seen  in 
the  telescope  by  reflection  from  one  face  of  the  prism. 

Absorption  Spectra. — We  have  already  seen  that 
colored  substances,  as  red  or  blue  glass,  absorb  all  the 
light  of  certain  wave-lengths  which  falls  upon  them. 
It  has  been  found  that  bodies  which  when  heated  to 
incandescence  emit  waves  of  a  certain  length  will  when 
cooler  absorb  waves  of  the  same  length,  just  as  a 
tuning  fork  will  absorb  the  vibrations  sent  off  by 
another  fork  of  the  same  pitch.  This  is  easily  shown 
by  the  following  experiment.* 

Light  Absorption  by  Sodium  Vapor. 

LABORATORY  EXERCISE  143. — A  glass  bulb,  as  an  air 
thermometer,  with  a  stem  of  three  or  four  millimeters  bore 

*  It  is  recommended  that  this  be  shown  by  the  teacher. 


396  PHYSICS 

has  a  piece  of  sodium  of  the  size  of  a  grain  of  wheat  and  a 
little  gasoline  put  into  the  bulb.  It  is  then  heated  over  a 
flame  until  the  gasoline  is  boiled  away,  leaving  the  bulb  filled 
with  gasoline  vapor  in  which  sodium  will  not  take  fire.  The 
stem  is  then  closed  by  a  piece  of  rubber  tubing  and  a  pinch- 
cock,  and  the  bulb  is  further  heated  in  the  yellow  sodium 
flame  in  a  dark  corner  of  the  room.  When  the  sodium  in 
the  bulb  boils,  its  vapor  will  appear  black  in  the  light  of  the 
sodium  flame,  but  colorless  in  the  daylight  or  the  light  of  an 
ordinary  lamp.  The  light  of  the  sodium  flame  is  completely 
absorbed  by  the  sodium  vapor,  while  the  same  vapor  is  per- 
fectly transparent  to  light  of  other  wave-lengths. 

THE   SOLAR   SPECTRUM 

The  Sun's  Spectrum  not  Continuous.— The  Solar 
Spectrum  when  seen  by  the  naked  eye  through  an 
ordinary  prism  or  grating  seems  continuous.  We 
accordingly  conclude  that  sunlight  has  its  source  in  a 
very  hot  solid  or  liquid  body.  But  if  the  Sun's  spectrum 
be  observed  by  means  of  a  spectroscope  with  a  very 
narrow  slit  and  a  telescope  of  sufficient  magnifying 
power,  the  spectrum  will  be  found  to  contain  many 
dark  lines,  showing  that  certain  wave-lengths  of  light 
are  absent  from  it.*  Thus,  at  the  particular  wave- 
length of  sodium  light  a  dark  line  is  seen,  indicating 
that  there  is  no  light  of  this  wave-length  in  the  solar 
spectrum. 

Fraunhofer's  Lines. — The  dark  lines  of  the  solar 
spectrum  are  called  Fraunhofer's  Lines  because  they 
were  first  described  by  Fraunhofer,  though  some  of  them 
had  been  previously  observed  by  Wollaston.  Thou- 
sands of  these  lines  can  be  seen  when  the  spectrum  is 
highly  magnified,  and  nearly  all  of  them  are  found  to 

*An  ordinary  direct-vision  spectroscope  will  show  these  lines,  and  it 
is  also  useful  for  observing  the  character  of  other  emission  and  abcorp- 
tion  spectra. 


OPTICS  AND  RADIATION  397 

be  of  the  particular  wave-length  of  the  gas  spectrum  of 
some  known  element  on  the  Earth.  Thus,  over  two 
thousand  of  them  are  found  to  agree  in  wave-length 
with  lines  observed  in  the  gas  spectrum  of  iron.  If  the 
Sun  is  a  hot  solid  or  liquid,  how  may  we  account  for 
these  lines  ? 

Theory  of  the  Sun's  Spectrum. — The  accepted 
explanation  is  that  the  Sun's  spectrum  is  an  absorption 
spectrum,  that  is,  a  continuous  spectrum  from  which 
certain  wave-lengths  have  been  absorbed  by  passing 
through  some  gaseous  medium  between  the  Sun  and 
the  Earth.  The  only  known  gaseous  media  which 
may  be  concerned  in  this  absorption  are  the  atmos- 
pheres of  the  Sun  and  of  the  Earth.  That  part  of  the 
absorption  which  cannot  be  caused  by  the  Earth's 
atmosphere  is  accordingly  attributed  to  the  atmosphere 
of  the  Sun.  Presumably,  many  of  the  elements  which 
are  in  the  solid  or  liquid  state  upon  the  Earth  are 
heated  above  their  boiling  point  on  the  Sun,  and  their 
vapors  constitute  the  Sun's  atmosphere,  as  air  and 
water  vapor  make  up  the  main  part  of  the  Earth's 
atmosphere.  In  passing  through  this  cooler  vapor, 
some  of  the  light  from  the  Sun's  surface  is  absorbed, 
just  as  the  light  of  the  sodium  flame  is  absorbed  by  the 
cooler  sodium  vapor.  By  this  means,  we  conclude 
that  sodium  vapor  exists  in  the  Sun's  atmosphere, 
and  hence  that  the  element  sodium  is  found  in  the 
Sun. 

This  theory  is  further  strengthened  by  the  fact  that 
the  bright,  flame-like  projections  around  the  edge  of 
the  Sun's  disc  give  the  bright-line  spectra  of  gases,  and 
that  these  bright  lines  correspond  in  wave-length  with 
the  dark  lines  in  the  absorption  spectrum  of  the  Sun. 


398  PHYSICS 

Composition  of  the  Sun. — The  spectroscope  accord- 
ingly enables  us  to  determine  the  composition  of  the 
Sun's  atmosphere,  and  by  that  means  to  judge  of  the 
composition  of  the  Sun  itself.  The  element  Helium 
was  first  discovered  in  the  Sun  by  means  of  its  spectrum 
and  afterwards  was  found  in  the  Earth.  More  than 
half  of  the  known  elements  have  been  identified  in  the 
Sun's  atmosphere. 

STELLAR   SPECTRA 


Absorption  Spectra  of  the  Stars. — The  stars  also 
have  spectra  resembling  more  or  less  closely  the  spec- 
trum of  the  Sun.  In  the  yellowish  stars,  as  Capella, 
Arcturus,  Aldebaran,  the  spectra  are  very  similar  to 
that  of  the  Sun  and  in  some  cases  the  two  are  apparently 
identical.  In  the  white  stars,  as  Sirius  and  Vega,  the 
absorption  lines  of  the  metals  seen  in  the  Sun's  spec- 
trum are  very  faint  or  invisible  and  the  blue  and  violet 
parts  of  the  spectrum  are  much  stronger  than  in  the 
yellowish  stars.  In  some  of  the  stars,  especially  the 
stars  of  Orion,  an  absorption  line  appears  in  the  blue 
which  does  not  belong  to  any  known  substance,  and 
which  is  absent  from  the  Sun's  spectrum. 

Photographs  of  Stellar  Spectra. — Fig.  122  is  from 
a  photograph  of  the  solar  spectrum  and  the  spectra  of 
several  stars.*  The  striking  resemblance  between  the 
spectrum  of  the  Sun  and  that  of  Capella  is  shown  by 
photographing  them  side  by  side  on  the  same  plate. 

OPTICAL   INSTRUMENTS 

Two  Kinds  of  Optical  Instruments. — Certain  optical 
instruments,  as  the  Camera  and  the  Projection  Lantern, 

*  From  a  plate  in  Huggins'  "Stellar  Spectra,"  through  the  kindness 
of  Professor  W.  J.  Hussey,  of  the  Lick  Observatory. 


OPTICS  AND  RADIATION 


399 


are  used  for  projecting  real  images  of  luminous  or 
illuminated  objects,  while  others,  as  the  Telescope  and 
Microscope,  are  used  as  aids  to  vision. 


The  Camera. — The  camera  will  be  readily  under- 
stood from  the  experiments  on  refraction  through  a 
convex  lens.  Its  essential  parts  are  a  converging  lens 
and  a  screen  for  receiving  the  image,  while  the  camera 


400  PHYSICS 

itself  is  a  dark  box  arranged  to  shut  out  all  light 
except  that  which  enters  through  the  lens.  In  the 
camera  the  image  is  usually  formed  at  the  nearer  con- 
jugate focus,  while  the  object  is  at  the  more  distant 
focus.  The  photographic  camera  is  provided  with 
some  device  for  exposing  the  sensitized  plate  or  film 
where  the  image  to  be  photographed  is  focused  upon  it. 

The  Projection  Lantern. — In  the  projection  lantern, 
the  object,  usually  transparent  and  strongly  lighted 
from  behind,  is  placed  at  the  nearer  conjugate  focus  of 
the  lens,  while  its  enlarged  image  is  projected  upon  a 
screen  at  the  farther  focus. 

Since  the  projected  image  is  much  larger  than  the 
object,  it  is  much  more  feebly  illuminated,  hence  a 
strong  source  of  light  is  needed  in  a  projection  lantern. 
The  best  light  for  this  purpose  is  the  electric  arc  or  the 
lime  light,  made  by  heating  a  piece  of  lime  to  incan- 
descence by  means  of  the  hydrogen  and  oxygen  flame. 

The  Eye. — The  human  eye,  regarded  as  an  optical 
instrument,  is  essentially  a  camera  with  its  lenses  so 
adjusted  as  to  form  real  images  of  external  objects  upon 
a  sensitive  membrane,  called  the  Retina,  which  lines 
the  back  part  of  the  eye.  The  box  of  the  camera  is 
composed  of  a  tough,  fibrous,  opaque  coat,  called  the 
Sclerotic  Coat,  in  the  front  of  which  is  the  transparent 
membrane  called  the  Cornea.  The  sclerotic  coat  is 
lined  with  a  black  membrane  called  the  Choroid  Coat, 
which  prevents  internal  reflections,  and  upon  the  inner 
surface  of  which  the  retina  is  spread  out. 

The  cavity  back  of  the  cornea  is  filled  with  a  watery 
fluid,  making  of  this  part  of  the  eye  a  converging  lens. 
Back  of  this  water-lens  lies  the  Crystalline  Lens,  a 
double  convex  lens  having  a  refractive  index  about 


OPTICS  AND  RADIATION  401 

equal  to  that  of  glass.  Back  of  this  lens,  the  main 
body  of  the  eye  is  filled  with  a  jelly-like  substance 
having  the  same  refractive  index  as  water,  and  which 
serves  to  preserve  the  shape  of  the  eye. 

In  front  of  the  crystalline  lens  is  the  Iris,  an  opaque 
curtain  with  a  circular  aperture  in  the  center,  called 
the  Pupil,  which  can  be  opened  or  closed  to  regulate 
the  quantity  of  light  received  by  the  eye  and  to  aid  in 
correcting  the  spherical  aberration  of  the  lenses. 

A  section  of  the  eye  is  shown  in  Fig.  123,  in  which 


-S 


FIG.  123. 

C  represents  the  cornea,  L  the  crystalline  lens,  /  the 
iris,  and  R  the  retina. 

Since  it  is  necessary  in  order  for  distinct  vision  that 
the  image  of  the  object  to  be  viewed  should  be  formed 
exactly  upon  the  retina,  it  becomes  necessary  to  'have 
some  method  of  focusing  the  eye  for  near  and  distant 
objects.  In  the  ordinary  camera  the  focusing  is  done 
by  changing  the  distance  between  the  lens  and  the 
screen  which  is  to  receive  the  image;  but  in  the  eye 
the  same  purpose  is  accomplished  by  changing  the  con- 
vexity of  the  lens,  and  thus  changing  its  focal  length. 

The    crystalline    lens    is    an    elastic     body,    and    is 


402  PHYSICS 

attached  all  around  its  edge  by  means  of  muscles  to 
the  sclerotic  coat.  When  these  muscles  contract  and 
pull  upon  the  lens  they  decrease  its  convexity  and 
accordingly  increase  its  focal  length.  This  changing 
of  the  focal  length  of  the  eye  to  adapt  it  to  vision  at 
different  distances  is  known  as  the  accommodation  of 
the  eye. 

Defects  of  Vision. —Since  the  principal  refraction  of 
the  eye  takes  place  when  the  light  enters  the  cornea, 
the  focal  length  of  the  eye  depends  largely  upon  the 
convexity  of  the  cornea.  If  the  cornea  be  too  convex, 
the  light  from  distant  objects  will  be  brought  to  a  focus 
before  it  reaches  the  retina,  and  when  the  lens  cannot 
be  sufficiently  flattened  by  its  muscles  to  correct  this 
defect  the  eye  is  said  to  be  near-sighted.  That  is,  only 
the  light  from  near  objects  whose  wave-fronts  are 
convex  can  be  focused  upon  the  retina.  To  correct 
this  fault,  concave  lenses  are  worn  in  front  of  the  eye 
to  increase  the  convexity  of  the  wave-fronts  which  pass 
through  them  before  they  enter  the  eye. 

If  the  cornea  be  too  flat,  then  the  light  waves  from 
near  objects  are  not  brought  to  a  focus  until  after  pass- 
ing through  the  retina,  hence  only  distant  objects  can 
be  distinctly  seen.  Such  an  eye  is  said  to  be  far- 
sighted.  This  defect  in  vision  is  corrected  by  wearing 
convex  lenses  in  front  of  the  eye  to  decrease  the  con- 
vexity of  the  wave-fronts  from  near  objects. 

Sometimes  the  cornea  is  not  truly  spherical  in  form 
but  has  a  greater  convexity  in  one  direction  than  in 
others.  Such  an  eye  is  said  to  be  astigmatic,  and  can 
be  corrected  by  wearing  an  astigmatic  lens  with  its 
greatest  convexity  at  right  angles  to  the  greatest  con- 
vexity of  the  cornea. 


OPTICS  AND  RADIATION  403 

The  Simple  Microscope. — A  single  converging  lens 
of  short  focus  is  often  used  as  an  aid  to  vision,  and  is 
known  as  a  Simple  Microscope.  Owing  to  the  fact 
that  the  lenses  of  the  eye  are  not  free  from  spherical 
aberration  and  do  not  exactly  focus  all  the  rays  from 
a  single  point  in  an  object  to  a  point  on  the  retina,  the 
image  of  a  point  covers  a  sensible  area  upon  the  retina, 
making  a  small  blur  instead  of  a  point.  For  points 
which  lie  very  close  together  these  blurs  overlap, 
making  an  indistinct  image.  If  the  object  under 
inspection  can  be  brought  very  close  to  the  eye  so  that 
its  separate  points  have  their  images  farther  apart  on 
the  retina,  this  difficulty  is  partly  overcome. 

But  when  an  object  is  held  very  near  to  the  eye  its 
wave-fronts  are  too  convex  to  be  brought  to  a  focus  on 
the  retina.  The  least  distance  from  the  eye  at  which 
an  object  can  be  distinctly  seen  without  a  special  effort 
to  accommodate  the  eye  is  different  in  different  indi- 
viduals, but  is  usually  about  25  centimeters,  or  10 
inches.  If  the  object  be  brought  nearer  than  this  to 
the  eye,  its  wave-fronts  are  too  convex  to  be  focused 
upon  the  retina.  The  purpose  of  the  simple  microscope 
is  to  lessen  the  convexity  of  the  light  waves  from  near 
objects  before  they  enter  the  eye, 

The  Microscope  as  an  Aid  to  Vision. 

LABORATORY  EXERCISE  144. — Hold  a  pin  in  the  fingers, 
and  looking  at  it  closely  with  one  eye,  bring  it  slowly  toward 
the  eye.  You  will  find  that  as  the  pin  approaches  very  near 
to  the  eye  it  looks  much  larger  and  that  it  also  becomes 
indistinct.  It  seems  larger  because  its  image  on  the  retina 
is  larger  than  is  usually  produced  by  a  body  of  its  size,  and 
it  becomes  indistinct  because  its  image  is  not  brought  to  a 
focus  on  the  retina. 

Hold  a  convex  lens  of  short  focus,  as  an  ordinary  botan- 
ical microscope,  close  to  the  eye  and  look  through  it  at  the 


4o4  PHYSICS 

pin  as  it  is  brought  near  to  the  eye.  You  will  find  that  the 
pin  can  now  be  seen  distinctly  much  nearer  to  the  eye  than 
before  and  that  it  accordingly  seems  larger  than  before. 
The  lens  renders  the  convex  wave-fronts  from  the  pin  less 
convex,  and  the  pin  can  accordingly  be  seen  until  it 
approaches  so  near  the  eye  that  its  wave-fronts  after  passing 
through  the  lens  are  more  convex  than  they  would  be  with- 
out the  lens  if  the  pin  were  at  the  least  distance  of  distinct 
vision. 

Make  a  pin-hole  in  a  piece  of  opaque  paper,  and  holding 
it  close  to  the  eye,  look  through  it  at  the  pin  as  it  approaches 
the  eye.  You  find  that  in  this  case  also  you  can  see  the  pin 
much  closer  to  the  eye  than  before.  This  is  because  the 
small  circular  area  of  a  wave-front  which  passes  through  the 
pin-hole  is  not  too  convex  to  be  focused  upon  the  retina. 
Observe  that  in  this  case  also  the  pin  seems  magnified. 

Hold  the  lens  in  front  of  one  eye  and  the  pin-hole  in  front 
of  the  other  and  look  through  them  at  the  page  of  a  book 
held  as  near  to  the  eye  as  it  can  be  distinctly  seen  through 
the  lens.  It  will  be  seen  that  the  letters  appear  almost 
equally  magnified  to  both  eyes.  The  lens  and  pin-hole 
accordingly  serve  about  equally  well  to  correct  the  spherical 
aberration  of  the  eye  for  very  convex  wave-fronts. 

Which  seems  nearer  to  the  eye,  the  page  seen  through  the 
pin-hole  or  through  the  lens  ? 

Which  is  seen  more  distinctly  ? 

From  which  does  the  eye  receive  more  light  ? 

What  advantages,  if  any,  has  the  lens  over  the  pin-hole  ? 

Magnifying  Power.- — Since  the  wave-fronts  which 
pass  through  the  lens  are  rendered  less  convex  than 
before,  they  seem  to  come  from  farther  back  of  the  lens 
than  the  object;  that  is,  the  apparent  distance  of  the 
object  seen  through  the  lens  is  the  distance  of  its  virtual 
image.  When  this  virtual  image  is  at  the  least  dis- 
tance of  distinct  vision  the  object  cannot  be  brought 
nearer  to  the  eye  without  rendering  its  image  on  the 
retina  indistinct. 

You  saw  in  looking  through  the  lens  and  the  pin- 


OPTICS  AND  RADIATION  405 

hole  at  the  same  time  that  the  object  seemed  equally 
magnified  by  both,  hence  the  object  seen  through  the 
lens  has  the  same-sized  image  on  the  retina  that  it 
would  have  with  the  lens  removed.  The  object  seen 
through  the  lens  seems  farther  away,  however,  than  it 
does  with  the  lens  removed,  and  it  accordingly  appears 
as  large  as  it  would  have  to  be  in  order  to  produce  the 
same-sized  image  upon  the  retina  if  it  were  at  the  least 
distance  of  distinct  vision. 

Since  the  more  convex  the  lens,  the  nearer  the 
object  can  be  held  to  the  eye,  it  is  plain  that  the  mag- 
nifying power  of  the  simple  microscope  is  greater  the 
less  its  focal  length. 

The  Compound  Microscope. — The  compound  micro- 
scope is  an  arrangement  of  two  or  more  lenses  for 
producing  a  greater  magnifying  power  than  is  possible 
with  a  simple  microscope.  Since  in  practice  it  is  very 
inconvenient  to  bring  the  object  as  near  to  the  eye  as 
would  be  necessary  in  order  to  see  it  through  a  very 
convex  lens,  it  is  customary  to  place  the  object  to  be 
observed  just  outside  the  principal  focus  of  a  convex 
lens  of  short  focus,  so  that  a  real  image  may  be  formed 
on  the  other  side  of  the  lens.  This  real  image  is  then 
observed  through  another  lens  used  as  a  simple  micro- 
scope. Thus,  in  Fig.  124,  the  small  convex  lens  (9, 
called  the  object  lens  or  objective,  forms  a  real  image 
of  the  object  AB  at  A' B' ,  and  this  image  is  observed 
through  the  lens  E,  called  the  eye  lens,  which  causes 
it  to  seem  to  be  at  A" B" .  In  practice  both  the  objec- 
tive and  eye  lenses  are  often  made  of  two  or  more 
lenses  in  order  to  give  a  greater  convexity  than  is 
possible  with  a  single  lens.  In  some  of  the  highest 
power  microscopes  the  objective  system  alone  consists 


/jo6 


PHYSICS 


of  as  many  as  ten  single  lenses.  Part  of  these  are 
concave  lenses,  and  are  used  to  correct  the  dispersion 
of  the  convex  lenses. 

The  Telescope. — In  the  compound  microscope  the 
object  is  placed  at  the  nearer  conjugate  focus  of  the 
objective  and  the  image  is  formed  at  the  farther  conju- 


FIG.  124. 

gate  focus,  making  the  image  larger  than  the  object. 
The  image  is  then  apparently  further  magnified  by 
means  of  the  eye  lens.  In  the  telescope  the  object  is 
at  the  more  distant  and  the  image  at  the  nearer  conju- 
gate focus,  hence  the  image  is  smaller  than  the  object. 
This  image  is  observed  through  an  eye  lens,  as  in  the 
compound  microscope. 

Construction  of  a  Microscope  and  Telescope. 

LABORATORY  EXERCISE  145. — Place  a  convex  lens  between 
a  lighted  lamp  and  a  ground-glass  or  greased-paper  screen 
as  in  Laboratory  Exercise  128.  Place  the  lens  so  that  the 
lamp  is  at  the  nearer  conjugate  focus,  and  make  the  image 
as  distinct  as  possible  upon  the  screen.  Place  another  con- 
vex lens  of  shorter  focus  on  the  other  side  of  the  screen 
where  the  image  can  be  distinctly  seen  through  the  screen 
when  the  eye  is  near  the  lens.  Observe  that  the  image  is 


OPTICS  AND  RADIATION  407 

larger  than  the  object,  and  that  it  is  still  further  magnified 
by  the  eye  lens.  Leaving  the  lenses  in  position,  remove  the 
screen,  and  look  through  both  lenses  at  the  lamp.  Observe 
that  the  image  of  the  lamp  is  apparently  seen  in  the  same 
position  and  is  apparently  of  the  same  size  as  when  the 
screen  was  used.  The  instrument  as  now  arranged  is  a 
compound  microscope. 

Replace  the  screen,  and  move  the  object  lens  farther  from 
the  lamp  so  that  a  reduced  image  is  formed  upon  the  screen. 
Remove  the  screen,  and  observe  the  lamp  through  the  two 
lenses  as  before.  The  instrument  is  now  a  telescope.  By 
removing  the  eye  lens,  you  will  observe  that  the  lamp  can 
be  viewed  through  the  object  lens  alone  by  placing  the  eye 
in  the  proper  position,  that  is,  at  the  distance  of  distinct 
vision  from  the  place  where  the  image  was  formed  upon  the 
screen.  The  eye  lens  accordingly  serves  as  a  simple  micro- 
scope for  viewing  the  image  formed  by  the  object  lens. 

The  Spy  Glass. — The  telescope  arranged  as  in  the 
preceding  exercise  is  known  as  an  astronomical  tele- 
scope, in  distinction  from  the  terrestrial  telescope  or 
spy  glass  used  for  viewing  objects  upon  the  Earth. 
Since  the  real  image  formed  by  a  convex  lens  is 
inverted,  the  astronomical  telescope  shows  objects 
inverted.  This  defect  may  be  corrected  by  introducing 
another  convex  lens  between  the  object  lens  and  the 
eye  lens  to  re-invert  the  image  formed  by  the  object 
lens.  In  the  ordinary  terrestrial  telescopes  two  convex 
lenses  close  together  are  generally  introduced  for  this 
purpose  because  by  this  means  the  re-inverted  image 
can  be  formed  in  a  shorter  telescope  tube  than  when  a 
single  lens  is  used. 

COLOR   VISION 

Young's  Theory  of  Color  Vision. — We  have  already 
seen  that  lights  of  different  wave-lengths  produce 
different  color  sensations.  We  have  also  seen  that  by 


4o8  PHYSICS 

combining  lights  of  different  colors  in  suitable  propor- 
tions the  sensation  of  white  light  may  be  produced. 
What  we  call  white  light  is  accordingly  not  a  simple 
color  sensation,  but  a  complex  sensation  resulting  from 
several  simple  sensations.  Most  of  the  other  color 
sensations  are  also  complex.  It  was  shown  by 
Dr.  Thomas  Young  that  any  color  sensation  could  be 
produced  by  the  mixture  in  suitable  proportions  of  light 
of  three  different  wave-lengths,  and  Dr.  Young  was 
led  from  this  fact  to  the  theory  that  in  the  eye  there 
are  produced  three  simple  color  sensations  which  are 
capable  when  suitably  combined  of  producing  all  possi- 
ble color  sensations.  These  three  simple  sensations 
are  red,  green,  and  blue-violet. 

Color  Blindness. — In  some  persons  the  eye  is  inca- 
pable of  producing  more  than  one  or  two  of  these  sen- 
sations, and  then  the  person  is  said  to  be  color  blind.. 
Thus  if  a  person  be  red  color  blind,  all  the  colors  he 
can  see  are  those  which  may  be  produced  by  the  com- 
binations of  green  and  blue-violet  light. 

COLOR   PHOTOGRAPHY 

Lippmann's  Process. — Several  methods  of  so-called 
color  photography  have  been  invented,  but  so  far  only 
one,  the  process  of  Lippmann,  is  true  color  photography. 
In  this  method  the  sensitized  plate  or  film  is  placed 
against  a  mirror  surface,  so  that  the  light  which  falls 
upon  it  is  reflected  back  through  it  again.  The 
advancing  and  reflected  waves  then  interfere  in  the 
sensitized  emulsion,  producing  a  set  of  standing  waves 
with  planes  of  interference  and  planes  of  greatest  vibra- 
tion, as  in  sound  waves  in  a  Kundt's  tube.  If  the  light 
be  all  of  a  single  wave-length,  these  interference  planes 


OPTICS  AND  RADIATION  409 

will  be  parallel  and  distant  from  each  other  by  half  a 
wave-length  of  the  light  used.  Since  chemical  action 
takes  place  in  the  emulsion  of  the  sensitized  plates  only 
where  there  is  no  destructive  interference,  the  silver  in 
the  plate  will  be  reduced  after  developing  only  in  these 
parallel  planes  distant  from  each  other  by  half  a  wave- 
length of  the  light  used. 

If  light  is  allowed  to  fall  upon  the  plate  after  it  is 
developed,  these  parallel  planes  of  silver  will  act  like 
the  reflecting  surfaces  in  the  Newton's  rings  apparatus, 
but,  being  at  the  same  distance  apart  everywhere,  the 
reflection  from  successive  surfaces  will  strengthen  one 
particular  wave-length  and  weaken  all  the  others. 
The  color  which  is  strengthened  will  be  the  one  whose 
wave-length  is  twice  the  distance  between  the  reflect- 
ing planes,  that  is,  the  color  by  which  the  plate  was 
originally  lighted. 

Ives'  Method. — Some  of  the  most  successful  methods 
of  representing  objects  in  their  natural  colors  by  means 
of  photography  depend  upon  the  discovery  of  Dr.  Young 
that  all  colors  may  be  produced  from  a  combination  of 
the  three  primary  colors,  red,  green,  and  blue-violet. 
In  the  Ives  photographic  process  three  negatives  are 
taken  simultaneously  on  the  same  plate  through  three 
color  filters  each  of  which  allows  light  of  only  one  of 
the  primary  colors  to  pass.  One  of  the  negatives  is 
accordingly  blackened  where  it  receives  red  light  from 
the  object,  another  where  it  receives  green,  and  the 
third  where  it  receives  blue-violet.  Since  each  color 
filter  absorbs  all  the'  light  except  the  one  color,  the 
parts  of  the  negative  which  do  not  receive  light  of  this 
color  are  not  blackened  at  all. 

Positives  are  then  printed  on  glass  from  these  nega- 


4io 


PHYSICS 


FIG,  135. 


OPTICS  AND  RADIATION  411 

tives.  Each  positive  is  black  except  where  the  nega- 
tive was  illuminated  by  light  of  one  of  the  primary 
colors,  but  is  transparent  where  it  was  lighted  by  its 
own  particular  color.  If,  now,  the  original  color  filters 
be  placed  over  the  positives  and  they  be  illuminated 
by  white  light,  one  of  them  will  show  the  red  parts  of 
the  picture,  another  the  green  parts,  and  the  third  the 
blue-violet  parts. 

Fig.  125  shows  three  photographs  taken  through  the 
three  color  filters.  The  upper  picture,  taken  through 
red  glass,  shows  the  strawberries  white  and  the  leaf 
black.  If  locrked  at  through  red  glass,  this  will  show 
red  berries  on  a  black  leaf. 

The  second  photograph  is  taken  through  the  green 
filter,  and  shows  the  berries  black  on  a  white  leaf.  If 
looked  at  through  a  green  glass,  this -will  show  black 
berries  on  a  green  leaf. 

The  third  photograph,  taken  through  the  blue- violet 
filter,  shows  both  the  berries  and  the  leaf  black,  but 
some  of  the  veins  in  the  leaf  are  white. 

If  the  three  pictures  be  projected  upon  a  screen 
through  the  proper  colored  glasses  and  superimposed 
upon  each  other,  the  first  will  give  the  red  berries,  the 
second  the  green  leaf,  and  the  third  the  bluish  veins 
in  the  leaf.  The  resulting  picture  will  accordingly  be 
in  its  natural  colors. 


APPENDIX  A 

Units  of  Electrical  Measure. — At  the  International 
Congress  of  Electricians  which  met  in  Chicago  in  1893 
the  following  definitions  of  electrical  units  were  agreed 
upon,  and  the  units  as  here  defined  are  known  as  the 
International  Electrical  Units. 

The  International  Ohm,  represented  by  the  resist- 
ance offered  to  an  unvarying  electric  current  by  a 
column  of  mercury  at  the  temperature  of  melting  ice, 
14.4521  grams  in  mass,  of  a  constant  sectional  area 
and  of  a  length  of  106.3  centimeters. 

The  International  Ampere,  represented  by  the 
unvarying  current  which,  when  passed  through  a  solu- 
tion of  silver  nitrate  in  water,  and  in  accordance  with 
the  specifications  laid  down  by  the  committee,  deposits 
silver  at  the  rate  of  .001 1 1 8  of  a  gram  per  second. 

The  International  Volt  is  the  electromotive  force 
that,  steadily  applied  to  a  conductor  whose  resistance 
is  one  international  ohm,  will  produce  a  current  of  one 
international  ampere. 

The  International  Coulomb  is  the  quantity  of  elec- 
tricity transferred  by  a  current  of  one  international 
ampere  in  one  second. 

The  International  Farad,  the  international  unit  of 
capacity,  is  the  capacity  of  a  condenser  which  is 

413 


4i4  APPENDIX  A 

charged  to  a  potential  of  one  international  volt  by  one 
international  coulomb  of  electricity. 

The  Joule,  which  is  equal  to  io7  ergs,  and  is  repre- 
sented by  the  energy  expended  in  one  second  by  an 
international  ampere  in  an  international  ohm. 

The  Watt  is  the  power  of  a  current  which  does  work 
at  the  rate  of  one  joule  per  second. 

The  Henry,  the  unit  of  induction,  is  the  induction  in 
a  circuit  when  the  electromotive  force  induced  in  this 
circuit  is  one  international  volt,  while  the  inducing 
current  varies  at  the  rate  of  one  ampere  per  second. 


INDEX 


INDEX 


Aberration,  chromatic,  367 

spherical,  351 
Absolute  temperature,  81 
Absorption,  of  radiant  energy,  177 

selective,  177 
Acceleration,  31 

in  circular  motion,  55 

of  falling  bodies,  32 

positive  and  negative,  32 

uniform,  31 

Accumulator,  electrical,  315 
Achromatic  lenses,  368 
Action  and  reaction,  39 
Air,  density  of,  64 

electrification  of,  277 

pump,  6 1 

thermometer,  81 

two  specific  heats  of,  188 

weight  of,  63 
Alternating  currents,  294 
Ampere,  the  unit  of  current,  302, 

413 

Amplitude  of  waves,  208 

relation  of  intensity  to,  226 
Angle  of  incidence,  346 

of  reflection,  346 

of  refraction,  358 
Anisotropic  bodies,  129 
Anode,  312 

Aqueous  humor  of  eye,  400 
Arc  lamp,  306 

Archimedes,  principle  of,  125 
Armature  of  magnet,  241 

coil  of  dynamo,  294 
Atmosphere,  electrification  of,  277 

pressure  of,  65 

standard,  70 

Atmospheric  pressure  and  respira- 
tion, 7Q 


Atmospheric    pressure,    measure- 
ment of,  67 

Atoms,  87 

Atwood's  machine,  29 
experiments  with,  30 

Audibility,  limits  of,  225 

Avogadro's  law,  90 

Barometer,  cistern,  68 
siphon,  70 

Barometric  height,  68 

Beam  of  light.  344 

Beats,  219,  233 

Bell,  electric,  289 

Bell  telephone,  299 

Bodies,  properties  of,  59 

Boiling,  114 

Boiling-point,  156 

influence  of  pressure  upon,  156 
influence  of  dissolved  substances 
upon,  159,  161 

Bound  charge,  257 

Boyle's  law,  78 

Bramah's  hydraulic  press,  117 

Brittle  solids,  134 

Bunsen's  photometer,  334 

Buoyant  force  of  gas,  94 
of  liquid,   122 

Caloric  theory  of  heat,  139 
Calorie,  183 

energy  value  of,  188 
Calorifier,  186 
Calorimeter,  183 

heat  capacity  of,  183 
Calorimetry,  183 
Camera,  399 
Candle-power,  336 
Candle,  standard,  336 

417 


4i8 


INDEX 


Capacity,  electric,  269 
Capillarity,  106 

Capillary     constant,   measurement 
of,  106 

tubes,  surface  tension  in,  106 
Capstan,  II 

Carnot's  theory  of  heat,  141 
Cell,  voltaic,  280 
Cellular  structure,  128 
Cells,  grouping  of,  318 
Center  of  gravity,  13 

of  oscillation,  22 

of  suspension,  22 

Centigrade  thermometer,  scale,  180 
Centrifugal  force,  56 
Centripetal  force,  56 
Charles's  law,  81 
Chladni's  plate,  200 
Chromatic  aberration,  367 
Circle,  motion  in,  37,  54 
Clouds,  electrification  of,  278 

formation  of,  165 
Coefficient  of  expansion,   cubical, 

149 

linear,  149 
tables  of,  150 
Coherer,  323 
Cohesion,  96 

between  solid  surfaces,  129 

magnitude  of,  108 

relation  of  surface  tension  to,  101 
Cold  produced  by  evaporation,  168 

produced  by  solution,  155 
Collision  balls,  41 
Color  blindness  408 

photography,  408 

vision,  407 
Colors,  complementary,  366 

of  bodies,  366 
Commutator,  294 
Complementary  colors,  366 
Composition  of  forces,  51 

of  a  uniform  velocity  with  a  uni- 
form acceleration,  47 

of  velocities,  46 
Compound  microscope,  405 

pendulum,  21 
Compressibility  of  gases,  77 

of  liquids,  109 

of  solids,  133 
Coneave  lens,  359 


Concave  mirror.  348 
Condensation  of  atmospheric  vapor, 
161,  164 

of  vapors,  115 
Condenser,  electrical,  260 
Conduction  of  electricity,  253.  275 

in  electrolytes,  312 

of  heat,  169 

of  heat,  law  of,  171 
Conductivity,  heat,  table.of,  172 
Conductors     and    non-conductors, 

253 

fall  of  potential  in,  275 
heating  of  by  current,  30x3 
loss  of  energy  in,  300,  307 
resistance  of,  300 

Conjugate  foci,  352 

Consonance,  233 

Conservation  of  energy,  143 

Convection  currents,  172 

Convex  lens,  359 
mirror,  347 

Cornea,  400 

Coulomb,  unit  of  electrical  quantity, 

3°3 

Coulomb's  laws  of  friction,  131 
Critical  constants  of  gases,  167 

pressure,  167 

temperature,  166 
Crystalline  lens,  400 
Crystals,  properties  of,  128 
Current,  alternating,  294 

the  electric.  283 

induction,  290 
Currents,  action  of  on  magnets,  284 

chemical  effects  of,  309 

heating  effects  of,  300 

primary  and  secondary,  291 
Curves,  magnetic,  244 

Dalton's  law,  85 

Daniell's  cell,  301 

Dark  lines  in  solar  spectrum,  396 

Davy's  experiment  on  the  nature 

of  heat,  140 
Defects  of  vision,  402 
Density,  determination  of,  125 

of  gases,  64 

of  liquids,  125 

of  solids,  change  of,  135 
Dew,  formation  of,  162 


INDEX 


419 


Dew-point,  162 

determination  of,  163 
Dielectric,  258 

capacity,  272 
Diffraction,  375 

grating,  378 

grating,  measurement   of  wave- 
length by,  380 
Diffusion  of  gases,  88 

of  liquids,  in 
Dipping  needle,  245 
Discharge,  electrical,  273 

electrical,    oscillatory    character 

of,  275 
Dispersion  of  light,  364 

in  lenses,  367 

Dissociation,  electrolytic,  311 
Dissonance,  233 
Distillation,  159 
Doppler's  principle,  227 
Double  refraction,  383 
Ductile  solids,  134 
Dynamical     equivalent     of    heat, 

189 

Dynamo-electric  machines,  293 
Dyne,  38 

Earth,  electric  field  of,  276 

magnetic  field  of,  245 
Echoes,  212 
Efficiency,  12 

of  electric  lights,  306 

of  engines,  196 
Elastic  fatigue,  135 

limit,  134 

impact,  41,  135 
Elasticity,  59 

Hooke's  law  of,  134 

of  gases,  60 

of  liquids,  99 

of  solids,  133 

of  volume  of  solids,  133 

perfect,  60 
Electric  attraction,  248 

bell,  289 

capacity,  269 

charge  of  earth,  276 

condensers,  260 

conduction,  253 

current,  281 

discharge,  273 


Electric  elasticity  of  the  ether,  258 

field,  257 

furnace,  307 

heating,  307 

lighting,  305 

lines  of  force,  258,  264 

machine,  253 

potential  265 

quantity,  268 

radiation,  320 

repulsion,  249 

resonance,  321 

spark,  273 

units,  301,  413 

waves,  320 

welding,  306 
Electrical  transmission  of  energy, 

307 
Electrification,.  249 

by  induction,  255 

of  air,  277 

of  earth,  276 

two  kinds  of,  251 
Electro-chemical  equivalents,  314 
Electrodes,  311 
Electro- magnet,  288 
Electro-magnetic  induction,  289 

telegraph,  288 

telephone,  298 

theory  of  light,  321,  391 
Electrolysis  312 
Electrolyte,  dissociation  of,  312 
Electrolytic   measurement  of  cur- 
rent, 312 

polarization,  314 

resistance,  316 
Electromotive  force,  268 
Electrons,  165,  274,  278,  394. 
Electrophorus,  256 
Electro-plating,  310 
Electroscope,  264 
Electrostatics,  248 
Electrostatic  series,  253 
Emission  theory  of  light,  344. 
Energy,  I 

conservation  of,  143 

kinetic,  18 

kinetic,  equation  of,  44 

potential  18 
Engine,  gas,  193 

heat,  189 


420 


INDEX 


Engine,    high    pressure    and   low 

pressure,  193 
steam,  190 
Equations  : 


E.M.F. 


M=mv  =  Ft.  ...45 


-2^....i7i 


T  — 107      . 

Ft 

v  =  at  =  — 45 

tn 


V*   :=-.      ..223 

v^  =  v(i  4-  bt}  ____  81 


Mv 


Equilibrium,  in  a  fluid,  120 
mechanical,  15 
of  solid  and  liquid  states,  129 
of  a  liquid  at  rest,  116 
Equivalent,  electro-chemical,  314 
Erg,  43 

Ether,  the  luminiferous,  properties 
of,  391 

as  a  dielectric,  258 
Evaporation,  113 
Expansion,  of  gases,  60,  80 

coefficient  of,  81 
of  solids,  147 
of    solids,    linear    and   cubical, 

149 

of  water,  146 
table  of  coefficients,  150 
Eye,  400 

Fahrenheit's    thermometer    scale, 

180 

Falling  bodies,  29 
Fall  of  potential  along  a  conductor, 

275 
Faraday,  discoveries  in  electrolysis, 

313 

discovery   of  specific    inductive 

capacity,  271 
Fatigue,  elastic,  135 
Field,  electric,  257 

magnetic,  240 
Floating  bodies,  124 
Fluid,  60 

classes  of,  60 

mechanics  of,  1 15 
Fluorescence,  326 
Focal  length,  350 
Focus  of  concave  wave-front,  350 

principal,  350 
Foot-pound,  2 
Force,  35 

constant,  38 

equation  of,  38 

moment  of,  5 

units  of,  38 

and  work,  42 
Forces,  composition  of,  51 

graphical  representation  of,  52 

parallelogram  of,  51 

resolution  of,  53 

triangle  of,  50 


INDEX 


421 


Forced  vibrations,  21 1 
Foucault'spendulum  experiment,  23 
Fraunhofer's  lines,  396 
Freezing  mixtures,  155 
Freezing  point  of  salt  solutions,  155 
Friction,  cause  of,  130 

coefficient  of,  130 

laws  of,  131 

rolling,  132 
Frost,  formation  of  164 
Fulcrum,  4 

Furnace,  electrical,  307 
Fusion,  151 

change  of  volume  in,  153 

latent  heat  of,  152 

Galvanometer,  286 
Gas  engine,  193 

equation,  82 

thermometer,  180 
Gases,  60 

buoyant  force  of,  94 

compressibility  of,  77 

convection  currents  in,  172 

density  of,  64 

diffusion  of,  88 

expansion  of,  60,  80 

expansion  coefficients  of,  8 1 

heat  conduction  in,  171 

kinetic  theory  of,  96 

laws  of,  77 

liquefaction  of,  167 

molecular  structure  of,  87 

pressure  of,  cause,  91 

relation  of  volume  to  pressure,  77 

relationof  volume  to  temperature, 

79 

specific  gravity  of,  64 

specific  heats  of.  187 

velocity  of  sound  waves  in,  223 

work  done  in  expansion  of,  84 
Gearing,  12 

Grating,  diffraction,  378 
Gravitation,  24 

acceleration,  magnitude  of,  32 

and  falling  bodies,  29 

and  time  of  pendulum,  25 

Newton's  law  of,  34 

pressure  within  a  liquid,  118 

pressure  of  liquid  column  inde- 
pendent of  its  shape,  120 


Gravitational  waves,  205 
Gravity,  center  of,  13 
Guinea  and  feather  tube,  26 

Hand  glass,  72 
Harmonic  series,  232 
Heat,  137 

caloric  theory  of,  139 

capacity,  183 

Carnot's  theory  of,  141 

conduction  of,  169 

engines,  189 

latent,   152,  168,  184 

measurements,  178 

mechanical   equivalent   of,   142, 
189 

mechanical  theory  of,  143 

nature  of,  139 

sources  of,  138 

specific,  186 
Heating  of  houses,  174 
Height  of  barometer,  68,  70 
Helmholtz,  233 
Hertz's  waves,  321 
Hooke's  law,  134 
Horse-power,  12 
Huyghens's    construction   for   the 

wave-front  of  light,  338 
Hydraulic  press,  117 
Hydrogen  thermometer,  180 
Hygrometer,  164 

Ice,  latent  heat  of  fusion  of,  184 

melting  point  of,  180 
Iceland  spar,  383 
Images,  real,  351 

virtual,  341 
Impact,  elastic,  41,  135 

inelastic,  136 
Incandescent  lamp,  305 
Incident  angle,  346 

ray,  346 

Inclined  plane,  9 
Index  of  refraction,  357 
Induced  current,  289 
Induction  coil,  292 

electric,  255 

electro-magnetic,  289 

magnetic,  246 

of  waves,  208 
Inertia,  26 


422 


INDEX 


Insulators,  254 
Intensity  of  light,  332 

of  sound,  225 
Interference  of  light  waves,  369 

of  sound  waves,  2 15 

of  waves  on  the  surface  of  liquid, 

373 
Inverse   square,  law   of,    34,   227, 

244,  333 
Ions,  280 
Isotropic  bodies,  129 

Jar,  Leyden,  260 
Joly's  photometer,  334 
Joule,  the  unit  of  energy,  302 
Joule's  determination  of  mechanical 
equivalent  of  calorie,  142,  189 
law,  303 
Jupiter,  eclipse  of  satellite,  330 

Kathode,  312 

rays,  325 

Kilowatt,  the  unit  of  power,  302 
Kinetic  energy,  18,  27,  44 

theory  of  gases,  96 
Kundt's  tube,  224 

Lamp,  arc,  306 

incandescent,  305 
Latent  heat  of  fusion,  152,  184 

heat  of  vaporization,  168,  185 
Lenses,  359 

achromatic,  368 

images  formed  by,  360 
Lever,  2 

as  a  machine,  4 

classes  of,  3 

laws  of,  3 

mechanical  advantage  of,  5 

moment  of,  5 
Leyden  jar,  260 

jar,  oscillatory  discharge  of,  322 
Light,  329 

diffraction  of,  375 

dispersion  of,  364 

double  refraction  of,  383 

emission  theory  of,  344 

intensity  of,  law  of  decrease  of, 
332 

interference  of,  369 

Maxwell's  electro- magnetic  the- 
ory of,  320 


Light,  nature  of,  389 

origin  of,  329 

periodic  character  of,  374 

polarized,  384 

rectilinear  propagation  of,  381 

reflection  of,  337 

refraction  of,  355 

undulatory  theory  of,  389 

velocity  of,  330 

waves,  332 

Lightning,  protection  from,  279 
Linear  expansion,  147 
Lippmann's  color  photography,  408 
Liquefaction  of  gases,  167 
Liquid  state  of  aggregation,  96 
Liquids,  buoyant  force  of,  122 

compressibility  of,  109 

density  of,  119,  125 

diffusion  of,  ill 

elasticity  of,  99 

form  of,  removed  from  gravita- 
tion, 99 

gravitation  pressure  in,  118 

properties  of,  96 

surface  film  of,  loo 

surface  tension  of,  105 

thermal  conductivity  of,  173 

transmission  of  pressure  by,  1 16 

viscosity  of,  109 
Lodestone,  237 
Lubricants,  use  of,  132 
Luminiferous  ether,  properties  of, 

391 

ether,  as  a  dielectric,  258 
Luminous  body,  329 

Machines,  2 

Magnetic  attraction  and  repulsion, 

239 

circuit,  241 
curves,  theory  of,  244 
field,  240 

field  of  current,  283 
field  of  earth,  245 
field,  strength  of,  247 
induction,  246 
induction  of  earth,  246 
lines  of  force,  241 
permeability,  239 
poles  of  magnet,  238 
poles  of  earth,  246 


INDEX 


1 


423 


Magnetic  poles,  rotation  of,  about 

a  current,  284 
Magnetism,  237 

terrestrial,  245 

Magnets,  natural  and  artificial,  237 
Magnifying  power  of  microscope, 

404 

Malleability,  134 
Mass,  27 

indestructibility  of,  27 

relation  of,  to  weight,  28 
Material  system,  35 
Matter,  I 
Maxwell's  electro-magnetic  theory 

of  light,  320 
Mechanical  advantage,  5 

equivalent  of  heat  unit,  142,  189 

theory  of  heat,  143 
Mechanics,  general  equations  of,  45 
Melting  point,  151 

point,  influence  of  pressure  upon, 

!54 
Mercury  barometer,  68 

compressibility  of,  109 

surface  tension  of,  107 
Microscope,  compound,  405 

simple,  402 
Mirror  reflection,  338 
Mirrors,  concave,  348 

convex,  347 

plane,  340 

spherical  aberration  in,  351 
Molecular  velocities  and  pressure, 

95 
weights,  95 

Molecules,  87 
Moment,  5 

of  pivoted  bar,  14 
Momentum,  37 

direction  of,  41 

persistence  of,  41 
Moon,  force  of  gravity  at  distance 

of,  33 
Motion,  circular,  37,  54 

Newton's  laws  of,  36 

quantity  of,  37 

rectilinear,  36 

resultant,  47 

uniformly  accelerated,  31 
Motions,  composition  and  resolu- 
tion of,  46 


Motions,  the  parallelogram  law  of, 

49 

Motors,  electric,  295 
Music,  physical  theory  of,  233 
Musical  instruments,  235 

scales,  235 

sounds,  225 

Needle,  dipping,  245 

magnetic,  238 
Negative  charge,  252 
Newton's  law  of  gravitation,  34 

laws  of  motion,  36 

rings,  369 

Nodes  and  loops,  214 
Non-conductors,  253 

Octave,  234 

Ohm,  the  unit  of  resistance,   302, 

413 

Ohm's  law,  302 
Optic  axis,  387 
Optics,  329 

Oscillatory  discharge,  275 
Osmosis,  112 
Osmotic  pressure,  112 
Overtones,  231 

Parallelogram  of  forces,  5 1 

of  velocities,  49 
Pendulum,   17 

center  of  oscillation  of,  22 

center  of  suspension  of,  22 

compound,  21 

energy  of,  17 

Foucault's  experiment,  23 

isochronism  of,  20 

laws  of,  20,  21 

length  of,  23 

persistence  of  plane  of  vibration 
of,  23 

reversible,  23 

simple,  21 

Permeability,  magnetic,  239 
Photometers,  333 
Photometry,  333 
Physics,  i 
Physical  universe,  I 
Pin-hole  microscope,  404 
Pitch  of  screw,  1 1 

of  tone,  227 


424 


INDEX 


Plate,  Chladni's,  200 

vibrations  of,  200 
Polarization,  electrolytic.  314 

of  Hertzian  waves,  386 

of  light,  383 

by  reflection,  387 
Polarized  light,  385 
Poles  of  magnet,  237 

magnetic,  of  earth,  246 
Positive  charge,  252 
Potential,  electrical,  265 

gravitational,  44 

energy,  18 
Poundal,  38 
Power,  II 
Pressure  exerted  by  a  gas,  91 

of  the  atmosphere,  65 

of  a  liquid  due  to  gravitation,  118 

transmitted  by  liquid,  116 

within  a  soap  bubble,  70 
Primary  coil,  291 

colors,  365,  408 

current,  291 

Principle  of  Archimedes,  125 
Prism,  triangular,    dispersion   by, 

364 

triangular,  refraction  by,  363 
Projection  lantern,  400 
Psychrometer,  169 
Pulley,  fixed,  6 

mechanical  advantage  of,  8 

movable,  7 

Pulleys,  systems  of,  8 
Pump,  air,  61 

force,  76 

lifting,  75 

Quality  of  sounds,  228 

Radiant  energy,  absorption  of,  177 

energy  and  heat,  176 

energy,  reflection  of,  177 
Radiation,  176,  329 

and  absorption,  178 

Becquerel,  391 

electric,  320 

kathode,  325 

Roentgen,  324,  39° 

visible  and  invisible,  389 
Rays  of  light,  344 
Rectilinear  propagation  of  light,  381 


Reflection,  angle  of,  346 

at  curved  surface,  346 

laws  of,  346 

at  plane  surface,  340 

of  light  waves,  337 

of  sound  waves,  212 

regular  and  irregular,  337 

total,  361 
Refraction,  angle  of,  358 

of  light,  355 

at  curved  surfaces,  358 

at  plane  surfaces,  355 
Refractive  index,  357 
Resistance,  electrical,  300 

electrolytic,  316 

of  cells,  316 
Resolution  of  circular  motion,  54 

of  forces,  53 

of  velocities,  53 
Resonance,  209 

electric,  321 

in  Ley  den  jar  circuits,  321 
Resonators,  209 
Respiration,  70 
Resultant  motion,  47 

of  two  forces,  5 1 

velocity,  50 
Rigid  body,  60 
Rigidity,  60 

Roemer's  determination  of  the  ve- 
locity of  light,  330 
Roentgen  radiation,  324,  390 
Rumford's  experiments  on   nature 
of  heat,  139 

photometer,  333 

Screw,  II 

Selective  absorption,  177 

Siphon,  74 

barometer,  70 
Siren,  201 
Soap  bubble,  pressure  within,  7° 

bubble,  pressure  of  surface  ten- 
sion on,  103 

Soap  film,  pressure  of  surface  ten- 
sion on  opposite  sides  of,  104 

film,  surface  tension  of,  101 
Solar  spectrum,  396 

spectrum,  dark  lines  in,  396 
Solids,  crystalline,  128 

properties  of,  127 


INDEX 


425 


Solids,  structure  of,  127 
Solenoid,  magnetic  field  of,  287 
Solution,  energy  changes  in,  155 
Solutions,  boiling  point  of,  159 
Sound,  199 

definitions  of,  224 

interference  of,  215 

nature  of,  224 

reflection  of,  212 

velocity  of,  in  air  and  glass,  224 
Sounds,  classification  of,  224 

limits  of  audibility  of,  225 

musical,  225 
Spar,  Iceland,  383 
Spark  discharge,  273 

discharge,  oscillatory   character 

of,  275 
Specific  gravity,  64 

gravity  of  gases,  64 

gravity  of  liquids  and  solids,  125 

heat,  186 

heat,  measurements  of,  186 

heats  of  gases,  187 

inductive  capacity,  270 
Spectacles,  402 
Spectra,  absorption,  395 

continuous,  393 

emission,  392 

of  chemical  elements,  393 

stellar,  398 
Spectroscope,  394 
Spectrum,  365 

absorption,  395 

analysis,  392 

continuous,  393 

dark  lines  in,  396 

emission,  392 

infra-red,  390 

of  sun,  397 

ultra  violet,  390 

Sphere  of  molecular  attraction,  102 
Spherical  aberration,  351 

waves  of  light,  332 

waves  of  sound.  227 
Spy-glass,  407 
Stable  equilibrium,  15 
Stability,  measure  of,  16 
Standing  waves,  213 
Stars,  spectra  of,  398 
States  of  aggregation  of  bodies,  59 
Steam  engine,  190 


Storage  cells,  315 

Strings,  velocity  of  transverse  wave 

in,  221 

Sublimation,  161 
Sun,  composition  of,  397 

spectrum  of,  394 
Surface  tension  of  liquids,  100 
tension  and  cohesion,  101 
tension  and  curvature  of  surface, 

103 

tension,  equation  of,  107 
tension,  measurement  of,  105 

Telegraph,  electro-magnetic,  288 

Telegraphy,  wireless,  324 

Telephone,  298 

Telescope,  406 

Temperature,  absolute  scale  of,  81 

absolute  zero  of,  81 

critical,  166 

lowest  known,  168 

measurement  of,  178 

sense,  137 

standard,  83 
Tension  of  surface  film,  100 

of  vapor,  97 

Terrestrial  magnetism,  245 
Thermometer,  calibration  of,  182 

construction  of,  179 

graduation  of,  180 

fluid  for,  179 
Thermometric  scales,  180 
Thermometry,  178 
Torricellian  vacuum,  68 
Torricelli's  experiment,  68 
Total  reflection,  361 
Tourmaline,  384 
Transformers,  297 
Transmission   of  pressure  by  liq- 
uids, 116 

Triangle  of  velocities,  50 
Tuning  fork,  interference  of,  216 

fork,  vibration  of,  216 

Undulatory  theory  of  light,  389 
Unstable  equilibrium,  15 

Vapor  pressure  or  tension,  97 
pressure  of  boiling  liquid,  114 
pressure  of  water,  158,  163 


426 


INDEX 


Velocity  of  light,  330 

of  light  in  glass,  356 

of  sound  in  air  and  glass,  224 

of  waves  in  strings,  221 
Velocities,  composition  of,  46,  50 

parallelogram  of,  49 

resolution  of,  53 

triangle  of,  50 
Ventilation  of  houses,  174 
Vibrations,  forced,  211 

of  bells,  220 

of  columns  of  gas,  200,  209 

of  plates,  200 

of  sounding  bodies,  199 

of  strings,  221 

sympathetic,  209 

transmission  of,  201 
Virtual  image,  341 
Viscosity,  109 
Vision,  color,  407 

defects  of,  402 
Vitreous  humor,  400 
Volt,  301 
Voltaic  cell,  280 

cell,  internal  resistance  of,  316 
Voltameter,  313 
Volume,  change  of,  in  melting,  153 

of  gas  dependent  upon  pressure, 

77 

of  gas  dependent  upon  tempera- 
ture, 79 

Water,  boiling  point  of,  158 
compressibility  of,  109 
density  of,  125 

dissociation  of,  by  current,  311 
expansion  of,  179 
latent  heat  of,  vaporization  of, 

i85 

surface  tension  of,  108 
thermal  conductivity  of,  171 


Water,  vapor  tension  of,  1 58,  163 
Watt,  the  unit  of  power,  302 
Wave,  204,  332 

amplitude,  208 

-front,  206,  332 

-front,   Huyghens's  construction 
for,  339 

induction,  208 

-length,  207 

-length,    measurement   of,    376, 
380 

-length  of  sodium  light,  381 

machine,  205 

-motion,  203 

-motion,  equation  of,  222 

-motion,  two  forms  of,  204 

spherical,  207,  332 

train,  207 

velocity,  220 

velocity  in  air  and  glass,  223 
Waves,  compressional,  204 

gravitational,  205 

interference  of,  213,  215 

reflection  of,  212 

standing,  213 

transverse,  204 
Weight,  24 

relaxation  to  mass,  28 
Wheel  and  axle,  10 
Windlass,  n 
Wireless  telegraphy,  324 
Work,  I 

done  by  expanding  gas,  84 

equations  of,  43 

measurement  of,  2 

units,  2,  43,  302 

Young's  theory  of  color  vision,  408 

Zero,  absolute,  81 
potential,  267 


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in  a  narrow  or  so-called  'practical '  way." 

Literature:  "  The  distinguishing  traits  of  these  papers  are  open-minded- 
ness,  breadth,  and  sanity.  .  .  .  No  capable  student  of  education  will  overlook 
General  Walker's  book ;  no  serious  collection  of  books  on  education  will  be 
without  it.  The  distinguished  author's  honesty,  sagacity,  and  courage  shine 
on  every  page." 

The  Boston  Transcript:  "  Two  of  his  conspicuous  merits  characterize  these 
papers,  the  peculiar  power  he  possessed  of  enlisting  and  retaining  the  attention 
for  what  are  commonly  supposed  to  be  dry  and  difficult  subjects,  and  the  ca- 
pacity he  had  for  controversy,  sharp  and  incisive,  but  so  candid  and  generous 
that  it  left  no  festering  wound." 

HFNRY  HOI  T  &  TO        29  West  23d  St.,  New  York 
nClNIM    nVofLl    CX  ^>\J.      378  wabasfc  Ave.,  Chicago 

v  *•« 


!   '  \-    I    \'   I  <  1  .  L 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 
BERKELEY 

Return  to  desk  from  which  borrowed. 
This  book  is  DUE  on  the  last  date  stamped  below. 


2  Nov'49CS 


1969  s?8 

8  1973 
RECD  LD 


3EC  2 '69 -9PM 


LD  21-100m-9,'48(B399sl6)476 


16830*1 


